Geese will protect their own goslings and be scary ferocious about it. They protect their own nest, although not nearly as aggressively as they protect goslings. They protect nothing else.
They could care less if a fox takes your chickens (good riddance) unless the fox foolishly tries for a gosling.
Geese are all noise and bluff. They aren't really warriors. Any predator, including the tiny weasel, can kill a goose.
Mid size and smaller hawks won't try them and probably won't try to take a chicken out from under their bills. But since mid size and smaller hawks don't take chickens except for baby chicks and young bantams, that is of limited value.
The value of geese is that they will set up a loud alarm if anything is out of the ordinary. They don't miss anything, not even at night. That gives you a chance to get outside with your shotgun to do the protecting yourself.