SLP here. There is anecdotal evidence that meds for depression, anxiety, etc. do impact stuttering. In some people, these medications reduce the stuttering; in others, it has been reported to actually increase the disfluency level. Depends on the specific medication and/or individual. To my knowledge there hasn't been any official research on this one way or the other. Informal consensus seems to be "Yes, it can have an effect." Anyway, just to provide a scientific tidbit, or lack thereof I suppose!