Is anything preventing non-US citizens from illegally registering to vote in non-Voter-ID states? [duplicate]

Let's say a non-US citizen (legal or illegal immigrant) is resident in the US and has a valid postal address in a state without "Voter ID" laws. Would anything prevent such a person from registering to vote in federal and state elections?

There is a related question on impersonating a registered voter, but I'm interested in the process of becoming a registered voter in the first place.