I have two cats.
One (in my avatar) was completely petrified by even the day old chicks. He wouldn't enter or exit the house through the breezeway while they brooded out there. He would literally shake in fear anytime he had to be near them.
The other is a cat I got from a neighbor's barn. She catches birds mid-air, she gets between 4 & 6 chipmunks & assorted critters a day.
I was, for obvious reasons, more concerned about her. (She averages 2 birds a week, even with a bell on her collar.)
She would sit on the breezeway & watch them in the brooder box, tail flicking, for hours but never did anything more than laugh at her friend Smokey for being so scared.
Now Smokey is not scared of them, and wants to be around them all the time. He runs up when it is treat time for the ducks and chickens and tries to eat the banana or peas or whatever it is with them. He helps me clean their coops and I have noticed he gets a lot more critters to drop at my feet lately.
Beullah, my other cat, still loves to lay there, tail flicking, and sometimes seems like she is stalking them, but never tries anything more than a few tender steps toward them. She does like to poach the birds who love to move in to the duck coop for a free meal, and she is never far away from them, but has never tried to attack them.
I think the chickens and ducks trigger a lot of excitement in the cats. They flap, take dust bathes, run all over in their noisy little packs, attract mice & other tasty treats. Also, I think my warrior cat would have more trouble than she could handle against my most docile hen. I would be very concerned if it were a feral cat - especially here, those Maine Coon cats are huge -but I think most times the cats are fantasizing more than plotting.
I don't think we should ever be cavalier. There is always a chance of predation from animals whose personality you don't know. But I would think that 4 chickens vs. 1 cat would a fair fight. I think Smokey knew that from the day they were popped into the brooder. I have a feeling Beullah agreed.
My grandfather had a problem with a cat harassing his aviary - he kept doves and homing pigeons - and he planted himself in a chair with one of my early supersoaker guns and a jelly jar of bourbon every night for a week. The cat took 2 nights of soaking & never returned. (My grandfather was a nice guy, but got some real enjoyment out of tormenting the predators & pests at his farm. I still pity the deer that would try to get at his garden, and the squirrels... HA!)