It would bother me. I am there to learn and with your scenario I am struggling to understand the content. Tbh I find it hard to envisage this scenario. A teacher has so many tools to hand. They have videos, work books, a whiteboard to draw on etc. all are very effective ways to get their points across. Generally speaking, people that stutter increase confidence and fluency as they become more proficient. I would expect a teacher to continue to stutter but not on every word or sentence and not to the detriment of their job.