No because a) "illegal immigrant" is not a term with a meaningful legal definition in the first place and b) Although sss.gov says undocumented immigrants need to register under their FAQ, their chart of acceptable documentation effectively excludes the exact population. https://www.sss.gov/wp-content/uploads/2020/02/Documentation...

But since those who entered without inspection have almost no way to show when they actually entered, full stop, and ICE doesn't actually have a comprehensive and reliable way of tracking the population that wouldn't run afoul of the Constitution, it's basically a violation that is effectively performative. The people this targets are not eligible for any benefits whatsoever on the federal level for themselves anyway (but still have to pay taxes) and cannot naturalize so there's no carrot and no viable stick. It's a rump piece of legislation.