I know of more than a few people with speech impediments, and the general rule of thumb is that if you are a good troop, no one fooks with you. However, if you are a shitpump, behind your back you will get it. Hang on, that's the general rule of thumb for everybody in the military ;D
I wouldn't sweat it. I know plenty of people who can speak "normally" but constantly jam their foot in the mouth with the out-there things that they say, which is infinitely worse than something that you really have little control over, such as a speech impediment. I would say that a few unenlightened people (such as those that point and laugh at handicapped people) might give you grief, but they are generally so thick that you can quickly cut them down to size (even if it takes a few seconds longer). A quick mind is better than a quick mouth, and when you join, you want to minimize on how much you speak anyways. A good instructor will take into account if you have difficulty with your speech when it takes you longer to answer a question, much in the same way if you ask someone (a Francophone, for example) something in English, and the time it takes them to translate, formulate a response, translate that into English, and then respond in English. No worries.
Al