From the horses mouth
HI,
I am quite "lucky" that I can speak from experience. I am currently doing my PPL and have recently done my first solo, but also I have a slight speech impedament. Whilst I do not know the severity of yours for me I can be speaking normally to someone and then for no known reason words just won't come out, extremely annoying and frustrating.
However, when Im using a radio either at work or whilst flying it seems to subcide and whilst my instructor is aware of it i haven't had a bout of it whilst i've been solo. Part of me thinks its a mental thing part of me doesn't know what the hell is going on sometimes, but as long as you can stay cool don't panic about it you can get by just fine.
Hope this has been of some help.