I don't see why you would get rejected because of a stutter. As long as the communication takes place and the flight goes smoothly. They want you to fly the plane well, its not a job that focuses on perfect articulate speech like a news anchor or public speaker. If your fluency is improving, then that's a really good sign. Why not get a taste of it now? Get a flight simulator and do some online roleplaying with your friends. Your friend can act as the ATC and you can be the pilot. Talk over headsets, and see how it hoes :)