No, Mexico is over-populating like crazy. The government of Mexico will not allow its economy to grow such as to provide for its young person population. Therefore, the young peasants (surplus population) are moving en-mass to the USA to find a better life. If those illegal Migrants were still in Mexico the population of Mexico would be skyrocketing as would be the birth rate.
Statistics and truth contradict everything you say. Mexico had a high birthrate in decades past, but not anymore. That is why you don’t see the high influx of Mexicans that you did in years past.:
https://www.csis.org/analysis/smaller-wealthier-mexico-horizon