I must admit I have no deep knowledge of stuttering, but I always thought it was a psychological thing. So if you teach someone a sign language, will they continue stuttering? On the same note, are there native sign language speakers who stutter?
I imagine that a failure of connection between brain and hands is possible though. We wouldn't call it "stutter" normally (it would probably surface as some kind of tremors), but effectively it would be a sign language alternative to stuttering.
Reminded me of the podcast Terrible, Thanks for Asking called T-T-T-Today, Junior. I couldn't find it on the official site cause it's not very well designed for search. I'm assuming my link will give the same content I originally heard. It was pretty heartbreaking.
If it's psychological, it might happen sort of. We are quite prone to subconscious suggestions, so someone in a susceptible state of mind could perhaps convince themselves to unintentionally create such a type of stutter.
My brother had a stutter. It's a bit psychological and a bit just technique. A lot of people can learn to drop their stutter with physical therapy and speech training, like my brother did. I doubt a stutter could even manifest in sign language with the exception of other issues that cause involuntary hand movement (like tourettes or other disorders that come with tics or muscle spasms), considering it's not a problem in the brain but somewhere between the brain and your mouth/lungs. But nobody would call that a stutter.