Unless your cat is a fat lazy type like Garfield, it stands a better chance of survival than you do, the cat is much better at stealth hunting than a dog and certainly a much better scavenger.
I could envision feral cats in the FO3 world, quiet, fast, vicious and deadly.
Keep in mind that cats don't run down their prey, they ambush and hunt, using trees, and long grasses. Even a Cheetah in the Savannah is unable to successfully capture alot of food if it's spotted too early, and its unable to sustain long distance running that it's prey usually can. How many big bushy trees and long paddocks of reeds did you see in *any* of the Fallout games? Human crops would be about the only place you could so such a thing. Hiding/hunting in a cave is more likely to make them wind up as Radscorpion food.
Think about it. Your tom cat Jerry. He doesn't run down the ally way swatting birds out of the air with his great speed, he stalks it from either a ledge or somesuch and pounces on the thing. Feral cats are simply just bigger, far more aggresive and able to take down bigger prey.
Dogs are scavengers, not hunters, so they would not survive without humans presence. Of course, they can live as stray dogs, but without humans trash, etc they would die. Cats in other hand, can hunt their own food.
You are an idiot, please read something on animal behavior or the very least watch a discovery channel documentry on dogs before giving remarkable insight to the nature of dogs and their inability to survive independently (because we all know dogs didn't exist at all before domestication).