I've been on the same product twice with several years inbetween, and the reaction I had was different between the two periods. My stutter was not at all affected the first time, but the second time, I was having odd little breathing irregularities while speaking, which could be said to influence my stutter (obviously not in a good way, though). So, mental health? Yes, that's what they're made for, and that's where they'll have an effect. But stutter? Nope, that's not what they're made for. If there's perhaps an indirect effect of improving moods and thus being better off with regards to stuttering, that's a different thing.