Stuttering is often incorrectly mistaken for nervousness. Stuttering can make some people unconfident. It's a negative association stutterers would likely want to separate from as it adds to stigma. That said, it's not without some basis in reality. So yeah it probably is a negative trope. I personally don't find it disrespectful for a fluent person to have a stuttering character as long as they're being respectful. Bottom line is you guys can do what you want in your own game, and if it results in the player interested and learning more about stuttering, all the better I'd say.