Yeah, they can get crabby if they feel crowded. 10 sq ft per bird is recommended space for a enclosed run. In the coop itself, they are generally supposed to have 4 sq ft of floor space per bird. I have a couple of cats, and they won't mess with a full grown chicken, so I would think they...
From what I've read here, you are keeping the birds in an enclosed run. How big is this run? The recommended minimum size, for an enclosed area, is 10ft per bird. And that, IMO, is on the small size. If chickens are crowded, they will attack each other.