Yes, I’ve seen that birthrates have fallen in Mexico more rapidly than for Mexicans or Mexican-descended citizens of the U.S. It’s an interesting trend.
One analysis I read was that most migrants to the U.S. are essentially the rural poor from Mexico. Rural tends to equate to higher birth rates, while urban residents have fewer children. Thus the illegal immigrants were most likely to be those with the highest birth rate at home, and the disproportionate migration of that high fertility demographic here is why Mexico’s rate fell so fast.