It is less obvious than some have assumed that, were the body of Jesus to be found, this would imply the undermining of Christian faith in the resurrection. There are two main reasons for this.
1) The Romans used to burn the bodies of martyrs, hoping thereby to impede the resurrection by scattering their bodies' original components. Those who are persuaded this method of preventing resurrection doesn't work will not necessarily be troubled if they find Jesus' body remained in the tomb, or was thrown to the dogs, or was burned, or whatever. However, that does make resurrection a theological rather than or more than a historical claim, which some may find troubling (while others may find it a relief!).
2) Paul, in 1 Corinthians 15, emphasizes that the seed that is planted is not the same as the body that grows out of it, which is at the very least compatible with an understanding of resurrection that doesn't require the body to leave the tomb.
My response to his remarks are as follows:
Isn't it the policy around here that you agree that if you claim the "Christian" label, you consent that your beliefs are fully in accord with the Apostle's Creed? Well, all this arguing for a non-physical "resurrection" simply doesn't mesh with the part that says "I believe in... the resurrection of the body." (Apostles Creed 8-11) In that case, you should just be honest with everybody and change it to the "Christian (other)" label, which encompasses all heterodox Christian belief systems. As to your two points, I say the following:
1. Actually, these Roman desecrations of Christian martyrs' bodies strongly suggest that early Christians were fully talking about the resurrection of the body, and were understood by the world around them to be talking that way too. We have little, if any, evidence that very many Romans lied awake at night wondering "Oh my gods, what if these Christians really started rising from the dead and walking around the city? It would be like a George A. Romero zombie movie!" Ok, so I made up the later part about zombie movies, but we do have plenty of evidence for Pagans attacking Christianity on the grounds that, because dead bodies get really gross in their graves, having said bodies get up and start walking about is hardly a desirable afterlife, if it's even a logical possibility. In this context, then, Roman tactics like burning the bodies of Christian martyrs who placed their hope in the resurrection of the dead and then spreading them over the Rhine river seems to be a kind of brutal reductio ad absurdum argument that says in effect: 'See, this is how mangled and disjointed dead bodies can get. Perhaps you should think twice about aligning yourselves with this seditious treason in the hopes of this misguided notion of the resurrection of the body because of this Jesus of Nazareth.' In this context, then, it seems likely that if the Romans were aware of any more compelling direct evidence that Jesus was not, in fact, risen from the dead, they'd have no qualms about ponying it up for similar brutally demoralizing displays.
2. Remember what I said about Pagan criticisms of resurrection on the grounds that putrifying bodies don't lend themselves to a very robust hope for a future reembodied life? Well, granted Pagans following Plato and Pythagoras believed in reincarnation, but there we are talking about freshly born bodies rather than decaying bodies, which is an important distinction. So now in the context of an early Christian community in the midst of the Hellenististic city of Corinth, a community facing serious identity issues in it's relation to the surrounding world, we read that "some of you say that there is no resurrection of the dead," (1 Corinthians 15:12) and ask "How are the dead raised? With what kind of body will they come?" (1 Corinthians 15:35) This segment of "Christians", in other words, have rejected the notion of resurrection on similar grounds to the surrounding Pagan world, and it is up to Paul to defend it's credibility. To this end, Paul takes the following approach in his argument leading up to the passage you cite:
A. (1 Corinthians 15:1-11) Establish strong logos for the resurrection of Jesus in an impressive array of witnesses, including himself, who have had experiences of the risen Jesus in ways that are downright empirical. At the same time, link this to the community ethos by reminding everyone that this is the Gospel preached by Paul and all the other apostles, the Gospel he indeed preached to the Corinthians, a Gospel rooted in personal experience. Indeed, Paul reckons Jesus' appearance to him was so startling and unexpected, it was like an unborn child suddenly torn from his mother's womb. (1 Corinthians 15:8)
B. (1 Corinthians 15:12-19) Strengthen the previously established logos by logically linking the resurrection of Jesus to the general resurrection. Further strengthen this logos by arguing that a world in which Jesus is not risen from the dead is a world in which the Christian worldview is completely untrue and downright useless. Worse still, because Paul and the other apostles have testified that God raised Jesus from the dead, if Jesus is not risen from the dead, they have born false witness about God (1 Corinthians 15:15), and so cannot escape God's wrath against deceivers who lead the Holy people astray (uh oh!). Indeed, if it is because of Jesus' sacrifice that the gentile believers expect their sins to be forgiven because of the covenant made through Jesus' sacrifice, but God has not ratified that covenant by raising Jesus from the dead, then the Corinthian church itself would amount to little more than a bunch of misguided people who mistakenly thought God forgave their sins and included them in the covenant blessings, but really remained in his wrath. It's noticible that as a converted Jew who believed in the general resurrection from the get go, for Paul the real question here is how Jesus, and by implication the Christian community, fit into this belief. If Jesus was not, in fact, risen, Paul is quite aware that he and the other apostles are so going to get it on judgment day. To be blunt, then, you may think the disciples had motive to steal Jesus' body and lie about it, but do really you think they would be willing to sell their birthright as Jews and go to hell for it? Personally, I'd reconsider: even a summary glance at the evidence from early Christian communities indicates that whatever happened with Jesus, it was enough to radically reorder their entire praxis as Jews around it.
C. (1 Corinthians 15:20-28) Reaffirm the logos that Jesus has, indeed, been risen from the dead, and link it to God's ultimate eschatological purposes for the defeat of evil, suffering, and death. In other words, say that this isn't just the pretty trimmings around Christian preaching that can be neatly unwrapped and disposed of, but the whole cornerstone of God's plan for saving planet earth. To be grossly but poignantly anachronistic about it then (for Jesus' reign endures forever), in times like these, if Jesus is not risen from the dead, we're all in very serious trouble.
D. (1 Corinthians 15:29-34) Remind the Corninthians that denial of the resurrection does not sit well with the enigmatic but apparently deep-seated practice of "baptism for the dead." The meaning of such rituals, after all, point symbolically toward that individual's resurrection. Build logos and ethos by reminding the Corinthians that Paul, the apostles, and Christians in general are taking great personal risks on behalf of this belief. And if it's that important, it's not exactly the kind of thing you'd want to sell out on.
And so, it is in this context that Paul gets to his discussion of the resurrection body against it's Corinthian detractors. For all your warped exegesis of Paul's metaphor of seedtime and harvest, which symbolically correspond to death, burial, and resurrection, you've forgotten two basic properties of horticulture. The first thing you have forgotten is that that which grows from a seed draws it's substance from what is planted. The second thing you have forgotten that form of what grows from the seed is deeply alalogous to the seed. It is indeed, contained in it's very essence. By implication, then, if a dead body planted in the ground is like a seed waiting to rise up for the harvest, then what is harvested on resurrection day takes it's form, substance, and essence from that body. All the same, Paul is more than aware that if resurrection day is going to be the greatest and most glorious day in human history, rather then a grotesque realization of George A. Romero's zombie movies, then there are going to have to be some serious changes to perishable human persons. As Paul himself puts it, "When you sow, you do not plant the body that will be, but just a seed, perhaps of wheat or of something else." (1 Corinthians 15:37) And so he begins his discussion by talking about different kind of bodies with different kinds of properties and capacity for glory. The current body has a certain kind of glory, but is sinful, mortal, and perishable. But then, it's important to note that not all bodies are the same - even in nature one kind of flesh differs from another. (1 Corinthians 15:39) So too, if there are perishable earthly bodies, there are also imperishable heavenly bodies capable of reflecting more glory (like angels, who are directly experienced with sense perceptions, which implies a certain tangibility, but dwell sinlessly in God's glory and never die).
And so Paul concludes: "So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body." (1 Corinthians 15:42-44) As easy as it would be to latch on to all this business about "natural" and "spiritual" bodies and jump up and say, 'Ah ha! Resurrection isn't really a physical kind of thing after all!', this would be a grave misreading of the text. The words often translated "natural" and "spiritual", for one thing, are psychikos and pneumatikos, derived from psyche (often translated as "soul" or "mind") and pneuma (often translated as spirit or Spirit). In other words, the difficulty with setting up this verse as a tension between between flesh and spirit is that both sides of the equation qualifying soma (body) weren't fleshly in the first place.
As N.T. Wright observes, "In 1 Corinthians 2.14-15, the psychikos person does not recieve the things of the spirit, because they are spiritually discerned, while the pneumatikos person discerns everything. There is, of course, no question there of 'physical' and 'spiritual' as appropriate translations... Thus far, the psychikos/pneumatikos contrast of verses 44-6 would have to be characterized as 'ordinary human life' contrasted with 'a life indwelt by the Spirit of God.'" (N.T. Wright, The Resurrection of the Son of God p. 349-350) Later, Wright goes on to observe that "In any case, the classical usage of pneumatikos well illustrates the meaning of what seems to be in Paul's mind. Aristotle speaks of wombs that are 'swollen with air,' hysterai pneumatika, and Vitruvius (first century BC) speaks of a machine 'moved by wind', pneumatikon organon. The adjective describes, not what something is composed of, but what it is animated by. It is the difference between speaking of a ship made of steel or wood on the one hand and a ship driven by steam or wind on the other." (Ibid. p. 352) Consistent with this interpretation, immediately after these verses Paul gives a discussion of Christ as the last Adam, a "life-giving Spirit" who breathes new life into Adam's dust. It would seem, then, that in the resurrection we are in for a fundamental change in our mode of existence to such a degree that Christ's Spirit will take on the animating and life-giving role our fallen mind currently does.
With all of these things in mind, I would encourage you to reconsider your current position, for it is no good thing to sell your birthright, and with it, the last hope for humanity. After all, to paraphrase David Bowie, it is a dreadful thing to come face to face with "the man who sold the world."