No there would be just as much ambiguity over "what is a Black person".
That is because actually whites, Asians, native Americans, etc., actually are all Blacks really, as far as chromosomes go.
The "Eve out of Africa" research proved that all races existed in and came from Africa, less than 100,000 years ago, which is not enough time for mutations to evolve.
So we are all just Africans, and we have inbred enough to bring out long existing recessive traits.
Another reason it is ambiguous is that instead of 51% Black being Black and 49% Black being white, it seem that any % Black was historically then considered Black.