Is it OK to stand on a pool table?

The answer is a definite no.

Please DO NOT STAND ON YOUR POOL TABLE! ... Mitchell pool tables are one inch 3-piece Brazilian slate. And while very heavy and sturdy, if too much weight is applied to the playing surface, the slate seams (where the pieces meet up) can pop loose and create a ridge or bump under the felt. This will require re-leveling of the table.