No, they cannot vote. To begin with. Period.
When someone gets to the polling station, they have to get on line for the right district, area, neighborhood... Then they give their name, and it is looked up in a book, then their signatures have to match. Then they get their ballot.
You can't vote at all unless you're registered and registered under your name.
And you get one vote. If people's votes were getting stolen, we'd be hearing about it. So the notion that an illegal got on line, got rejected, but used their photographic memory to remember a signature so they can come back and use it four years from now is highly unlikely. At least on a mass scale, massive enough to affect an election. If they were that smart they wouldn't be illegals to begin with. And quite frankly, I'm not sure how somebody can memorize somebody's signature upside down at a glance and successfully duplicate it in the next election - all this without the real owner of the name noticing that somebody's impersonating them and thus in the process blocking them from voting.