Perhaps -- it would be easier to scruitinize if the OP cited where their numbers came from. And given that the undocumented immigrants number is still off by more than a factor of 2, to me it reads more like it's just reactionary nonsense heresay rather than having any actual basis in reality. I'm open to being wrong though.

Also:

* I don't see any reason to believe nobody has more than one "cultural identity."

* Race is really more about culture than biology too. Maybe less so, but if for some reason you were motivated to come up with some categorization of people based on their biological ancestry, the races that we talk about wouldn't make a ton of sense. When you hear people saying that race is "socially constructed," this is what they're talking about. The Irish weren't considered white a century ago, and it's not like the change came about due to some scientific breakthrough.