Voter roles are registration are effective. I vote in almost every election, and they can tell my ballot status when I go in. My vote is tied to my address and other factors, so it seems like it would be clear if I wasn't a legal citizen.
I also have to show a government ID when I vote, but it doesn't seem like that's made a big difference in the security of the elections I participate in.
If the 400 cats (assuming domestic cats) can work together as a unit, then I believe they can do anything. Knowing cats, though, I'm going to back the other competitors.