My geese don't really hang out with the chickens. They tolerate the chickens in a remote kind of way, but if a chicken was being attacked I doubt they would do anything about it. I keep them fenced in a large moveable area but if they were all free range, it is more likely that the geese would be off eating grass on one field and the chickens would be over in the other dust bathing.
We have a local bald eagle pair, many many hawks/falcons, and owls . . . haven't lost a bird but the geese are only a small part of that. I use my moveable fence and always include trees inside the fence for cover, I provide covered areas for the chickens to run to, I keep the geese as lawn mowers / large lawn ornaments that discourage flying predators, and I have roosters for the early warning calls -- they are better than the geese for alerting all the birds to danger. The geese will form a tight group and peer at the sky -- the chickens run for cover . . . the ducks will hang out with the geese sometimes or just clump together where ever they are. Our farm is also in the middle of hayfields and a river, slough, and seasonal ponds, with lots of other choices for dinner . . .
I've heard of male geese trying to breed with ducks. I think it has happened with chickens as well. Most places sell goslings in pairs, or as straight run, so you wouldn't really know what you would get. Or you could try to find a grown pair for sale locally -- in the fall many breeders have good quality geese available as mostly grown 6 month olds or so . . . With two females you won't have to worry about protective ganders during the breeding season - ganders are often more social than females though, so it would just be what you decided to go with. There are many breeds of geese / some more likely to be laid back and others more likely to be protective, so it is good you have time to research. The goose forum has lots of good information in the old threads -- I think there's even some about the chicken protection issue . . .
