The answer is "no".
That's not the correct question, though. The correct question is why non-believers such as those who funded these "experiments", find relics to be such a challenge and go to such lengths to try and discredit them?
We may not need relics to support our faith but atheists certainly need to discredit them to support their lack of faith.
As for the Shroud itself, science proves nothing. If the Shroud was genuine then it would have been witness to an event unprecedented in the annals of human and natural history; the resurrection of a dead body.
What physical and scientific phenomena accompany such an event? Is light and/or radiation emitted? Could this impact dating methods used to assess the age of the Shroud? We simply don't know. If you think science has all the answers to the Shroud, you're wrong.
Science is investigating an event which went beyond the normal laws of nature. In these situations it is blind.
For the same reason those that claim to believe go to such lengths to try and prove them "authentic". There is no real faith where a relic is required to prove an event.