In the 13 years I've been an ATCO I've never noticed a pilot stutter.
If you just leave pauses nobody will notice, we'll just think that you're thinking with the mic live.
There is one guy who flies for Sabre who is totally unintelligable. It sound as though he is deaf and has learned to speak without being able to hear. He only seems to do the RT at night though - have never heard him in the daytime. Wonder if he does the PAs as well...