Nope.
The law is clear.
I’m not even sure that the majority of illegals will sign up.
Many already have access to jobs, federal and state benefits such as schooling, health care, etc due to the thriving market in fake ids. By signing up they get the ‘green card’ but it also identifies them as an illegal.
By signing up they may be making the mistake of ‘coming out of the shadows’ and giving the future administrators of ICE their address and name which would make it easier to deport them or get them discharged from their jobs.