Almost without exception, I would agree with Matt that it's about being yourself. However, I don't have a problem with singing a specifically dialect song from your area with the local accent which is more like an exaggeration of the way in which you usually speak anyway.

I think using another language is usually a different matter, as that's about communication which possibly wouldn't otherwise take place, or is perhaps a matter of courtesy to the person you're communcating with. This would surely rarely apply with accents, as English-speaking people generally understand 'received' English because of mass communication, and unless one's accent is very broad have little difficulty in understanding other accents - dialect may be a different matter!

Barbara