Yes, but without proper documentation we won't know if they are legal eligible to vote.
Yet somehow we survived as a country without such requirements in the past.
But unfortunately, elections in this country are decided by who doesn't vote. And conservatives (i.e. Republicans) have recognized they they are the one who win when people don't vote. So they make it difficult for people who vote for Democrats to vote. That would be the poor, primarily. The primary attributes that poor people have in common are frequent address changes. So the "voter ID" laws are designed to disenfranchise anyone who has changed their address within a year of the election. You do that by putting the registration deadlines as early as possible. You have to show an ID to register, and if your address has changed by the election, you won't be able to vote. Especially because the Republicans are printing flyers threatening arrest if you show up with invalid ID.
Similarly, they disenfranchise students by making a gun registration form acceptable ID, but a student ID is not.
And, if course, that guy living in a doorway on main street isn't going to have valid ID even though he is as elligible to vote as the Mayor is. Maybe moreso, because if the mayor is a Republican, he's probably a felon.