On Conan's show, they are at least plugged in, though. When he picks it up and says something into it, it sounds exactly like you think it would. When he knocks it over, it makes a loud thunk.
they can and do, particularly if the guests are going to be moving around and doing things on stage. If they are going to be just sitting and talking a fixed setup of overhead mics is simpler than wireless lavaliers.