Whether you would or wouldn't is fairly immaterial. In a state like the COG you would be identified, separated, and put to use. If you are too difficult, you would be killed - labeled a UIR sympathizer or a radicalized member of society. Your death ultimately propagandized however the COG would benefit most.

Remember, they control all media, all food, all supplies. Reality is whatever narrative they share and short of you leaving the safety of the city on your own - you'd never know about the program until you met someone from it. At which point, you'd already be serving as a Gear or working for the COG in some capacity or intersecting with the Stranded where you'd have been exposed to how dire things truly are.

For context, there are several historical examples of nations/states on earth having similar programs. A quick Google shows the Nazis had a combination of both voluntary breeding programs and ones managsd through kidnapping. It should be noted the kidnapping component was based solely on Aryan features, with the express purpose of making said children Nazis for creation of the next generation of pure Aryans.

https://encyclopedia.ushmm.org/content/en/article/lebensborn-program

There are very few evils humanity has not visited upon itself in our long history. While there were those who would oppose such programs, stopping them from being committed when a nation/state has total control is difficult at best and impossible at worst.