First of all, absolutely not recommending that someone bring a cat in despite a No Pets policy.
However, having done it and lived very in a constant state of paranoia as a result, I wonder where all of these landlords who care about it have come from on this forum. The apartment-prior-to-buying-the-house was taken in an act on desperation, when we couldn’t find an apartment that would take a cat (very rare, at least around here - where are you guys finding them?) and our previous landlord did a bad enough job fixing things that we couldn’t live there another year (as in, we had a hole in the bottom of our shower for THREE WEEKS).
At first, we were convinced that the landlord would be knocking down the door any day, and we locked the cat into the bathroom with all of his stuff every time we knew that a maintenance guy would be by. Then we realized that there were six cats and two dogs living in our building alone, and that nobody else even tried to hide them, even when the inspectors came along. And we relaxed. We ended up staying there for a few years, since pet-allowing apartments are so rare and management could obviously care less.
My general impression of that rule was that they only cared if they were looking for a reason to throw you out. Same with the rules about grills on the porches and parking boats in the parking lot, for that matter. Pretty lax.
FYI - to the best of my knowledge (having seen several neighbors move out over that time period), they replaced the entire carpet whenever someone moved, regardless of the condition and whether or not they were sneaking in pets.