Could race-mixing have helped prevent "white genocide"

Imagine that there is a small population of people of some race of people who have an extremely high fertility rate. If whites were to segregate themselves from them, then the population of this people would grow out of control, eventually growing equal to the population of whites, and then surpassing it. Now the white population is insignificant compared to the population of this fertile race, and white genes are endangered when compared with the genes of this race - i.e. "white genocide" is inevitable.

But if whites were to assimilate with this people from the beginning, and the white race were to swallow up the genes of this fertile race early on, then the genes of the fertile race would be an insignificant drop in the white gene pool.

Based on this principle, I wonder if it would have helped preserve the white race if whites had assimilated with Mexicans more early on. Now the US is overrun with immigrants from Mexico, but I wonder if it would have been less of a problem if the Mexicans had immigrated and assimilated with US Americans 100 years ago instead of today. Presumably the fertility rate of Mexicans over the last 100 years was more than that of Americans, so if you were to mix Mexico with America 100 years ago it would be less Mexican than if you were to do the mixing today.