Yes, some. At least half a dozen I could identify, and I could tell the difference between others without knowing where they are from. I imagine the average American might know 'posh English', 'Northern', Scottish and Irish.
I'm not trying to insult Americans, I just think typically the average American knows less about our accents than we do about theirs, probably because their media is more dominant and because we are small so look outwarRAB more.