Speech disabilites for PhD admission for international applicants
Provided he is fluent in written English, I cannot see how his application could legitimately (or legally) be discriminated against. If he can listen to a spoken conversation without problems, that will hugely decrease the concessions needed to accommodate his disability.

Provided he can listen to spoken English without a problem, I do not see why even giving presentations is an unreasonable expectation either. Why not do so in the style of Stephen Hawking, setting to the presentation slides a pre-prepared monologue that is read out by a speech synthesizer? If he is a reasonably fast typist, responding to questions should not be a significant problem either.

This style of communication could even be extended to taking tutorial classes, networking at conferences, etc. Sure, it's a bit awkward and people may take a little while to adjust. But it certainly seems doable.

Perhaps this is relevant reading: Is it possible for people with a stutter to have a career in academia?