No. Only because I do not believe that any holy object, except for all of Creation itself, has been left by God for Earthly possession, including the Shroud of Turin. Therefore as long as the Shroud's "Holy Authenticity" is always in question, it is quite safe from me.
However, the real crux of this discussion is not whether holy relics are safe from me, but rather is the World safe from the believers of the Shroud. Should the Shroud somehow prove to be authentic, would it become a banner about which to start a Holy War? The implications are enormous. Think about. That's why the 2nd. Commandment exists and why Moses destroyed the Ten Commandments Tablets that were wrought by God on Mt. Sinai. This act by Moses is an allegorical example that nothing made by God is to be be possessed on Earth for reasons of mans own good.
The Shroud of Turin is only a harmless, Medieval relic, as long as it is only regarded a symbol for what it represents and does not become "Holy Unto Itself".
You raise this question, impugning the motives of Shroud researchs and "believers", without a shred of evidence that such a thing would happen. If it proves to be authentic (an event I doubt can occur) WHY do you think it would it become a "banner about which to start a Holy War?"