@Possum: Actually, not so much. Nonwhite American immigrants tend to do one of two things: either develop a unique accent that's influenced by the surrounding accent but clearly distinct (see: California Mexicans, Florida Cubans, Louisiana Cajuns, certain West Coast Asian/Pacific Islander groups) or work very hard to pick up the 'standard' American accent as heard on TV and radio (most African immigrants, Latinos and Asian/Pacific Islanders not living in large ethnically-homogeneous communities).

It's very unusual for a nonwhite American to speak with what would generally be recognized as a 'regional' accent. Other ethnic groups, when big enough, can have their own 'regional' accents - Black Americans, for instance (not even an immigrant community except in the same sense that all non-First-Nations are) have a family of accents that varies across regions, as do Mexican-Americans. But an outside listener - say, someone from Vermont - presented with audio of a black Texan speaking is much more likely to hear "black" than "Texas."

That's much less true in most of Canada. A black Newfie is pretty much indistinguishable from a white Newfie over the phone, and someone from BC will easily identify both as Newfies.