I have a friend who has a 'ground' stutter but mysteriously it does not manifest itself in radio communications airborne.
Probably has to do with combining brain functions.
I guess he has no time to stutter...no pun intended.
All your friend can do is try.
Start with gliding or other low(er) cost options and see how things develop.
Realistically communication is of crucial importance in a multi crew environment. Standard procedures, standard communications, non standard and emergency communications both with ATC and crew members.
But as I said there are many cases of no stutter when the brain is otherwise engaged.