Whatever the answer to that question, there is no reason not to examine the truth/falsehood of the Shroud. The truth cannot lead us away from Christ.
Sure it can. We believe by grace through faith - not by the tactile senses, but through the renewed mind's conceptualization of who Christ is and what He has done for us.
If Christ's entire wardrobe turned up on some mis-routed Bekins truck it would only serve to take Christians' minds off the prize who now resides in heaven and within the heart of each believer.
Resist the urge to touch the wound. He has risen -- the only sign we need.