Re: But can the camera recognize approved cats, or not?
SO l,ong as you have a decent sized gang of cats (and at least a couple of them are psycho ninja fighters) then intruder cats only break in once (& rapidly flee to lick their wounds)
Umm all cats are psycho ninja fighters. It's just whether they can demean themselves enough to bother to attack, or indeed take any interest at all in mundane items like the property of their human minions.
It's only if said intruder cast takes an interest in their stuff, and indeed if it's stuff they care about (for example the paper bag their latest expensive cat toy came in, as opposed to the toy itself) that things get active.
Somewhat like kids really...