Does accent really affect student understanding in class?

In my opinion yes accent of trainer/teacher does matter to students. I have been in situations where I had to present/train in multi-cultured audiences and soon I realized this that accent does matter. Proper standard accent eases audiences and relieves them from that extra effort they have to put to make the points intelligible.

Yes, it does. An unfamiliar accent can be extremely annoying. Visual displays such as video, whiteboard, are the best way to overcoming accent issues.