Yes, that is the case now, Ebarnacle, because in this civilization we live in we have already domesticated dogs and cats and they have thus become useful to us. Dogs have served mainly as guards and companions, for hunting other animals, and in war. Cats have served mainly as rodent catchers and as companions.

They would be of no use whatsoever to us, though, if we had never thought to domesticate them in the first place. We might then consider them as our competitors, the same way we now consider rats. Wild dogs and cats would certainly threaten our pets and livestock, and the dogs would threaten us directly.

Rats could also be useful as companions and pets to any society that chose to domesticate them and regard them as such. They are very smart and affectionate when they are domesticated and treated kindly.