Well, as long as we're talking scientifically - how would it prove that Christ rose from the dead? How does the shroud provide that evidence?
I accept that Christ rose from the dead after three days in the tomb. I accept that on faith. I don't need a receipt.
I think the Shroud can definately help unbelievers. It helped me, for instance.
Back when I started to investigate the claims of the major religions (this was just after I had rejected atheism) I proceeded in a scientific manner, examining evidence rather than going on faith. I did this because I was used to this method when I had accepted the nonexistence of God.
Having been born and nominally raised Catholic, I did have a familiarity with Christ's teachings and life, however with the knowledge I had I was not prepared to believe in any manner whatsoever.
That's when I stumbled across ShroudForum, a web site concerned with examining the Shroud. What I found was astounding. Evidence about the quite probable problems with Carbon-14 testing, the Sudarium, the general consensus with the scientific community that there is no natural causes that could have created the image, etc.
What was most shocking to me was this:
Speculation on how the image was formed is focused in theoretical physics models which for many implies (comfortably or uncomfortably) resurrection. For example, as Kevin Moran writes:
It is suggested that the image was formed when a high-energy particle struck the fiber and released radiation within the fiber at a speed greater that the local speed of light. Since the fiber acts as a light pipe, this energy moved out through the fiber until it encountered an optical discontinuity, then it slowed to the local speed of light and dispersed.
The fact that the pixels don’t fluoresce suggests that the conversion to their now brittle dehydrated state occurred instantly and completely so no partial products remain to be activated by the ultraviolet light. This suggests a quantum event where a finite amount of energy transferred abruptly.
The fact that there are images front and back suggests the radiating particles were released along the gravity vector.
The radiation pressure may also help explain why the blood was "lifted cleanly" from the body as it transformed to a resurrected state.
Now, I didn't wholeheartedly believe this scientific explanation (nor do I now, as it is just a theory) but it hit me so hard that I had to learn more about the historical evidence for Christ. This search led me to a variety of wonderful resources, and a long story short, I have reverted to the Church.