I'm on the back end side of things but I've been a professional developer for over 13 years. I definitely stuttered during the interview but I mentioned that I was nervous and my speech is normally much more fluid. As for my stutter being a problem on the job, it's normally not at all unless I have to give a presentation or something. I actively avoid presenting in front of large groups, which has probably held me back in a few instances because other colleagues weren't afraid to volunteer. When I do have to give a presentation I make sure I practice it beforehand and thankfully these are often free flowing enough I can substitute in the event of a block. I've worked with at least two other folks with a slight stammer/stutter in my organization. You can do it!