I'd go with unrelated as well, simply because of the amount my mouth has changed with years of braces (my palette was extremely narrow from sucking my thumb as a child, I even ended up with this metal contraption designed to push my teeth/palette apart). I'd hoped that MAYBE my speech would improve with more room in my mouth but it was wishful thinking. I'm sure stuttering is a psychological thing more than anything else but I could definitely be wrong.