Go for it! I did summer research programs like that in college and they were always a great experience - you get a much better taste of what research is like working full time rather than the few hours that can be fit in during the semesters. When giving science talks I usually will preface the talk by explaining that I have a stutter - I’ve found that it’s both helpful for me since there’s less pressure not to stutter, but also helps the audience to be more understanding! Good luck!