Ive never had a problem with my birds and the moggies. I dont think Ive ever seen a cat chase one of my chooks even when I had them free ranging right up to the house. Henry does come with me to see the chooks when I feed and water them, but as soon as they see him, they make a right old din and he scarpers as fast as his paws will carry him. I dont know whether having Jethro helps, as he is quite a large cockerel.
Freddie and Henry are very keen hunters of everything normally, but I have never worried about the chooks.