ducks (and other fowl) and cats

We have recently got ducks - 4 khaki campbell hens, adding 1 drake soon, and are planning to get a trio of Brecon Buff geese as well as a number of chickens in the next few months. At the moment the ducks are still scardy-ducks and dont leave their house much, they have a big house and a large static run, which we will expand. The plan is to make a completely fox-proof fence, and therefore presumably cat-proof as well but I am not sure. I plan to let the geese free range (over about 5 acres) during the day and keep them in the run at night, the ducks to live mostly in the run with outings to the garden and pasture, and the chickens probably to stay in the run. I would love to let them all free range but we have really bad problems with foxes and they will just get eaten, even during the day. We dont currently have a cat but we will be getting one (need one to keep rodents in check).

My concern is how the cat will treat the birds. I presume a fox-proof fence would be cat proof as well, but am I being naive? And what about when they are out and about - will a domestic cat stalk and kill poultry? Thanks for any thoughts on the matter!

We had the neighbor's cat kill a full sized Muscovy duck at our last place, and maimed at least three other birds that come to mind, I hated that SOB cat. We also have always had our own cats around our poultry. We have three cats now, they share food with the poultry and get along swell. But it could go the other way too. Our cats hunt and kill all sorts of stuff, but they never touch our baby rabbits, our baby chicks, anything of ours. Good cats.
not sure how helpful that is.
Our first cat was an adult feral cat we had adopted from Hawaii and had as a house cat for years before we ever got poultry and he became an indoor outdoor cat. He was perfect with our baby chicks, and adult poultry, but again, a great hunter at the same time. The three barn cats we have now we got as kittens and were raised in the barn, same thing. So, I don't even know I would say getting a certain age cat would make the difference.

It depends on the cat. We had hens and chicks in the suburbs - plenty of cats roaming around and they never bothered the birds. Then we got a tiny scrawny kitten and that one was a dedicated bird-killer and did kill the babies right out from under the hens. She didn't bother them over a certain size, tho (by the time they were fully feathered). I doubt a goose would tolerate a threatening cat in its territory. Our pullet cochins walked right up to the cat and pecked it on the face at their first meeting - showed the cats what's what and the cats left them alone. The bird-killer cat would like to hide and jump out and scare the ducks but never acted like she'd harm them.