I agree that the geese might not protect the chickens . . . mine wouldn't purposefully. On the other hand, they don't like small, furry, animals. My cats used to follow me into the chicken yard, but after dealing with the geese following them around with their heads down and hissing the cats gave it up as a bad idea. That wasn't during breeding season. Now, I think the gander would have done more than hiss, and I would be either short a cat, or have one with less fur and a reformed character. Since the cats already know that chickens are yummy, you might need a stronger deterrent . . . you can usually get live traps from the Humane Society to get rid of feral cats . . .
My geese are American Buff geese, and during the non breeding season most of my children can go in and the geese ignore them. During the breeding season -- no way. My 12 year old who feeds them is the only one that can go in reliably. Even my 9 year old gets a little intimidated by the big ganders rushing and hissing. A fence might be a good first step and then you can see . . .