Whether there's a link with stuttering and serotonin, I don't know. But serotonin syndrome is not really linked to having more serotonin naturally. Some people are more susceptible to it and the reasons why are not too clear (I'm in med school btw, so not an expert but I still know a bit). I'm sure there are plenty of stutterers who have suffered from depression and I'm fairly certain that their stuttering doesn't disappear when serotonin levels are low