Hm, mine has been sitting on a rock at the bottom of the tank for the past 1.5m I think. Actually, only it's ends have actually been on the rock. There is a gap under it's middle.
It's as happy as can be...constantly fluffed up, it's short tentacles looking for food. And it does eat well...very well!
Depends on the species, but the majority need to be on the substrate. Unlike other corals they can't be glued to anything so they tend to fall off and are easily injured. They also can move themselves around the tank on their own. So, similar to an anemone if he doesn't like where you put him, he'll go cruising around the tank till he finds a place he does.
I have seen them survive on rocks also. However, they do 'inflate' and their soft tissue can become irritated and damaged on the solid surface. As cyber says, they can move around the sandbed too. They inflate, deflate, and move around like that.