I don't see why not.
Perhaps the better question is what happens if you swap a non-Flying monster onto an obstacle that *isn't* a trap.
I'd assume it would be able to move off on its next movement action - but what if it has no valid paths off (not common in standard maps, but with a Cragheart in play, maybe)? Is it just permanently immobilised?
no, if a monster looses flying on an object it gets trap damage and is places on the nearest empty hex. so in this case this rule from the rulebook should apply.