Purely anecdotal. But I don't stutter when I impersonate someone, sing or go into fight or flight response. There is an idea that stuttering could be caused by the feedback loop in the brain listening to yourself speak and checking for errors and in situations where that gets turned off you don't stutter. My stutter is directly tied to my anxiety levels. I know if I'm stressed I stutter more and when I work on anxiety reduction then it improves.