My uncle has a moderate-to-severe stutter and he is a college professor. I've never been in his classes though, so I have no idea what that's like, but he must be ok if he manages to make a living from that. He's outgoing, is not afraid to speak his mind and stand up for himself when someone makes fun of his stutter and was involved in an affair with a student 20 years his junior (and he is far from good-looking), so the stutter is probably not the defining factor in his performance.