That's a good question. As far as I know, polyurethane doesn't react with coin metals and the adhesion mechanism for nano tape shouldn't be expected to leave any nasty residues. That said, I don't think it's a very common approach, so the amount of practical experience with this application might be limited. Personally, the only thing that would worry me would be leaving the unadhered part of the coin exposed to the elements but if that's not a concern then you might be okay.
Your best bet might be to select a few "sacrifice" coins to test this on for a few weeks before using it on anything you'd regret damaging.
