"Motor-voter laws automatically register you in many states when you get a drivers license. Yes, the voter is supposed to be a citizen but there is no requirement to provide proof."
I thought there were only two.  California and Oregon.  I'd have to double check Oregon's registration requirements but I remember California's requires either an SSN (which an undocumented would not have) or "legal presence."
Just a quick and dirty search from California's DL FAQ.
"State law requires every applicant for an original California identification (ID) card and driver license to show verification of birth date and proof of legal presence within the United States to help safeguard the accuracy and integrity of departmental documents."