I have a pair of geese, the gander is an american buff - considered to be one of the most docile geese breeds and the goose is a brecon buff. Raised and living with my runner ducks, the geese treat the ducks as their children. I have two coops of chickens and all the birds get free ranged together under supervision in the evening. My goose doesn't let the chickens get too close to her ducks, my gander only occasionally will stick that long neck of his out and make a move towards a chicken. The gander is a clown and full of mischief; I think he only does it for the fun of it. None of the chickens have ever been hurt by one of the geese. In fact, just last night one of my brahma pullets was running and screaming because she was being chased by a cockerel wanting to mate her. Not only did the head roo run over to chase the young upstart cockerel off, but my gander was the roo's back up.
All in all, I'd have to say they peacefully co-exist. I'm not sure the same would be true with a more aggressive breed of goose.
I added 2 geese to my flock when an Elderly couple needed to downsize their flock. A white Emden and Toulouse joined my flock this past fall. Lovely, beautiful and they all coexisted well....until this spring when they started laying eggs! I have one Indian runner duck (she lost her mate to a hawk a while back). My duck was in the stock tank swimming when I left one night....the next morning I found her entire head mangled and bloody. I wasn’t sure I could save either of her eyes and she was missing some skin on top of her head. I assumed off the bat she stayed 8n the water overnight somehow and an owl we have in our woods tried to get her. Well after isolating her and treating her wounds she regained sight in both eyes and her wounds healed...she happily joined the flock. 2 days later we found her huddled in the shed with half of her scalp peeled back and bloody. What the heck? It was at this time we noticed the geese would gang up on ANYTHING that went near their nest (we have dog igloos they like to lay in). We knew it wasn’t An owl any longer but the geese. We have witnessed them pinning down a chicken and needling her to no end if she got too close! So I penned both of them separately until their nesting is over for everyone’s safety! They are fierce protectors and I love them but...come on!