Maybe. I guess that's what happened with earlier waves of immigration. But the political climate is different now. You get points for identifying as a "minority," so if it matters, many "mixed: people may still identify as non-whites.
On that (you get points for identifying as a minority) we agree. So perhaps it would be good for “whites” to break up into “white Anglo-Saxons/Germanics”, “white Latin Europeans”, “white Slavs” etc. etc. - that way everyone gets to be a minority :)