You, me, him, her, them, those and everyone else around you who you interact with on a daily basis would agree that, no, if you break into a country illegally and shit out a kid while you're there, that kid is not magically entitled to that nation's citizenship and benefits. That was never the deal to begin with and its preposterous to insinuate that it was ever even part of the intention.
And they'll ignore it all the same.