We sort of "adopted" a stray cat recently. I won't allow it in the house (we already have a house cat) but we're feeding it outside. It's not feral or wild by any means, but I do not trust it.
A cat IS a PREDATOR. It's as simple as that.
Most cats (there are exceptions) will not bother full grown chickens but I would not allow their access to young/small ones. My ferals (whom I spay/neuter, feed, work on taming and eventually find good homes for) and tame kitties have all either been in love with or terrified of my chickens. None have ever done harm but I have always had adult birds.
Yup, they will pull their heads thought the fence and then eat them off. Been there done that. Ferals get a dirt nap if the so much as look at the chickens funny. I hate doing it, but there is a line in the sand on that one.
If there are as many cats as you say, then my guess would be YES they are going to be a problem. Feral cats can be vicious especially if they are trying to feed kittens. Lots of cats will rapidly decimate the prey population, and then your chickens are the prey. Invest in a live-trap and turn them over to your local humane society. Hopefully you don't live in one of those area where they just spay/neuter them and release them back into the wild.
Live trap them, then kill them. No need to burden (time and cost) the humane society with an animal that will not get adopted because of it's temperament. They will kill songbirds around your feeders too. There is not a niche for ferral cats in the wild.
I have 2 cats (young one and an old one) the old one doesn't seem to pay much attention to the chicks. The young one seems fascinated with them...and I just caught him inside their little yard. My husband "shushed" his little butt outta there and I went out and brought him in. He was hanging around and everytime he would get to close to them I would throw things at him and make alot of noise to run him off. When he was in the enclosure he was laying on top of a dog house watching them. I've been trying to just keep him in the house while they are out there. Hopefully it will get to the point that they're not so fascinating to him anymore...