I do to a certain extent (stutter, rather than stammer)but haven't found it a problem, expecially as most of the R/T is set piece phrases. My way of getting past any word that might be causing a problem, is to say something else instead, and once the flow is going the problem word comes out with no problems. Frequently it only needs and 'Um' or 'Err' to prefix the sentence to get it moving.
Haven't heard about some countries not allowing stammering pilots (shouldn't this Human Rights Act cover that?)