We have red-tailed and red-shouldered hawks, great horned owls, barred owls, peregrine falcons, barn owls, you name it. The daytime predators seem to go for the squirrels and of course the falcons like birds. The owls seem to come and go. I do believe that they hang around for the rats.
I'd bet money on it! Nature has a way of bringing all these creatures together in a balance.