Mine does!
Actually, Chico puts his mouth on the top of his right paw. He'll sit up and hold it up to his mouth like that, or sometimes he stretches out and rests his head on his paws but with the right paw up to his mouth. For all the world, looks like he is sucking his thumb, it is SO cute! Also, kind of seems like it is a "self comforting" thing that he does.
And he likes to sleep upside down under his wheel sometimes, too.
