Coming at it from the teaching side there is definitely a high correlation between lack of foreign accent and good teaching skills. In school I used to help assign graduate TAs into math sections. We would go through and rate all the graduate students by teaching skill and then use that to divide up teaching and grading assignments.

The data showed unambiguously that TAs who lost their accent were much better teachers than those who didn't. It wasn't about not being able to understand the words of the TA; there was an English qualification test that weeded out anyone who couldn't be understood clearly. I think the lack of accent was a proxy for other changes, like being adaptable and willing to alter one's behavior. The bad TAs with accents tended to use ineffective teaching techniques and not change while the good TAs updated their teaching methods based on feedback.