If everyone is free ranging (which geese need) it won't hurt to have some. Geese tend to make noise when unusual things happen. Chinese geese in particular are noisy.
There was a instance this spring when I found one of my chickens dead, with head wounds. The two geese were standing close, so I think what happened is that a hawk killed the chicken and the geese went over and were honking about it, which drove the hawk away. I know the geese didn't kill her, because there was never aggression towards her from them. Even if a hawk kills a chicken, they won't stay around to be able to eat it and soon will learn that it's not a good place to hunt.
I think Wilbur killed one of my EE hens early this summer, protecting his chicken girlfriend. He hasn't been aggressive toward anyone else, but was towards this chicken. I don't know why he didn't like this chicken and thought she was a threat.
Considerations to think about if adding geese for flock protection: extra food, extra bedding, is the housing large enough for chickens and geese together, or keep them in separate housing? enough green pasture for grazing, how bad of a hawk problem is there to warrant geese, do you like geese?