Depends how brushed up on the ADA the landleech in question is. Registered Service Animals have protections under federal law, but ESAs don't.
Most people dont know the difference and it's 100% legal to make a very Official Looking document stating your cats are Medically Nessicary ESAs and imply they really shouldn't discriminate over such matters without a lawyer.
I've gotten my cat (and my ex-roomate her malamute) into a couple of different apartments run by large managment companies this way. The leasing agents at the desk arent paid enough to deal with it.