Yes, it will work to offer cats as a bank perk for a new mortgage in Russia, because people like cats. There is nothing better than to invite a cat to live with you when you have a new home. When someone takes out a mortgage, the cat will help their house feel like home.
I feel that offering a cat would cause an increase in business. I feel that something this oddball and out their would do the bank good and cause them to have both positive and negative feedback. As they say, even bad publicity is good publicity. It will have people coming in to see what the hubbub is about, and might even get them to get a mortgage!
No I do not think that it will work to increase business. Buying a house is a big responsibility and commitment and so is getting a new pet. People would generally not want to take on both jobs at once. When people want to buy a house they are not looking for a pet.
I don't know much about Russian culture, but I don't think this will bring in more business with even the most superstitious. I also worry about what will happen with the cats after people open their accounts. They already have an abundance of stray dogs, I think most of these poor cats will end up on the street.