I think it's generally a good idea to use foam or something under the tank, mostly it just avoids imperfections causing stress points.
I don't think using a whole sheet should be an issue, but if you are really concerned about it, you could just cut out the center. -I've done this many times before, but mostly because I want to occasionally look at the bottom of the substrate (even though it's not terribly interesting).
Also, you don't need a piece that thick. I really don't think it will cause any problems, but you could go with a thinner piece if that was easier/cheaper.