Can a drained pool be pushed up out of the earth?

Yes. If you have a high water table, then water pressure will try to lift the pool out of the ground. Mostly this is going to be due to water (ground settling could also do damage), so it's less of a concern if you're in a flat, dry area, but even in that case it's still a possibility.

It's unlikely your pool has so much structural integrity that it would literally pop out of the ground. Much more likely is that it would crack or buckle from a lack of pressure equilibrium.