Yes a goose is a good animal to have to protect chickens.
You don't want a flock of geese though to protect chickens because the geese would likely bond with each other and lose interest in protecting your chickens.
But if you keep one goose around the chickens the goose will then more bond with the chickens and then will ward off any enemies of the chickens and keep the chickens protected and from harm.
My Grandpa used to raise chickens and he use to have a problem with some of the chickens getting killed and after he got a goose and kept the goose near the chickens he had no other issue with the chickens being killed by other animals.