I'm sorry but this is not correct. Cats may or may not kill chickens of various ages, but it has little to nothing to do with being well fed. Some cats retain more of the hunter instinct than others, that is very true, but cats that kill, do so whether they are hungry or not. Well fed cats are responsible for the deaths of millions of small animals a year.
We will have to agree to disagree then. My personal experience and observation has been that a hungry cat -- whether they are an avid hunter or not -- is more apt to explore more new angles of "is this food or not?".
Yes, cats that are hunters because they have a higher drive/instinct will always kill whether they are hungry or not. But there are plenty of cats that don't fall into that category. I grew up with tons of barn cats on the farm, have been active in feral TNR my entire adult life, and keep cats with my chickens. I've known plenty of cats that would sit there and watch a mouse walk right on past.
What it comes down to is the individual cat. The OP's best bet is to gradually introduce her cat to adult chickens under careful supervision and see how the cats react.