SLP here who has studied stuttering - the reason why this works is because your brain is focusing on the novelty of the accent, which lessens the frequency of stuttering in that instance. Many children who stutter will notice this and begin to use an accent to try to avoid stuttering. Sadly, the more this is done, the less novel it is, and stuttering will usually return to it's normal frequency. It is a really interesting effect, though! It can sometimes get you through a short period of time when you don't want to stutter, like an interview or a phone call.