I went to drama school with a stutter, since childhood and pretty severe. I didn't leave with one though. They \*drill\* speech exercises at least in conservatoires, and all acting courses will have some element of public speaking. The whole thing with stuttering for me was anxiety would make i hard for me to speak, however repeatedly standing in front of audiences and delivering lines to - at the beginning- - not great success taught me that you can fail, and survive. This is turn reduced anxiety and massively improved my speech longer term. You can also absolutely act with a speech impairment, I had a really bad lisp still leaving drama school and booked work on a fairly large broadcaster with an international reach. My speech difference was seen as a cool characteristic, not a downside at all. Now my speech is ''fixed'' I might liteally have to relearn my lisp for my next job.