Some maybe, just like some dogs. We have three cats and two dogs, all of which keep varments out of our yard and protect the chickens. But, stick a baby chick in front of our cats, and two wouldn't touch it. The other, I don't trust, but I equate that to handing an ice cream cone to a...
What about cats? This farmer neighbor with her rats you'd think we'd have issues too but we don't. We have 2 indoor-outdoor cats and two indoor-outdoor dogs, all of whom I am sure have something to do with why rats stay away.
Gosh, that's horrific! I saw you said you tried cornmeal. Did you try it 50-50 with baking soda? My farmer friend had issues and tried that, and she had more dead lying around than she even knew she had.