I believe this depends on whether the controls are reversible or not.
Certainly on the gliders I fly with simple push-rod connections to the elevator I get direct feedback through the stick on buffeting and the like, and I would expect to see the stick move if it weren't in my hand. It certainly springs back to a different position if I let go of it when I'm out of trim.
However, I've never actually seen it oscillate, as when I'm hands-off I'm usually in stable flight trying to pee into a bag.
