Hi...given the fact that the current floor is 12" squares, I would not consider 'entombing' them. You run the risk, and it is very risky, of the mastic used for setting new tiles degrading the adhesive of current squares. You then could have a huge problem.
Most 12" squares are not high-quality material and I would never assume they will not lift. To get the old stuff up completely (including remnants of old glue) takes a lot of scraping, but the result will last forever.