How long until we can be categorized as just plain ol' American?

Caucasian has really nothing to do with Caucasus mountains, it's just an anthropological identification of your race based mainly on the structure of your skull. Having said that, I agree with you. After three or four generations, you might as well be American, even though for some people race also defines cultural heritage and they may get offended at being pigeonholed into being American when their race and origins are clearly African, for example.