They will find other food far more easily.
Stanford once had something known as the Stanford Cat Network, now called the Feral Friends Network, which sounds like something from the Camp Wedontwantcha comic. This group caught feral cats left on campus and tried to find them homes. Some of the cats that were too feral to become cats ended up at the Stanford horse barn.
Some of the barn cats would hunt. I've been presented with a dead mouse. Others managed to get people to overfeed them, and they'd get fat and lazy. Once I saw a mouse, found a cat, and put the cat down near the mouse. The cat did nothing. Useless cats accustomed to free food were sometimes placed as house cats and replaced with new hunters. About four good hunting cats could clear the entire property of vermin.
You have to manage the cats to get results.
They aren't good at hunting rats in particular. Rats are big and cats are scared to fight them.
> Do feline predatory instincts have an upside? While New York’s feral cats kill lots of mice, they are no match for the city’s rats, which greatly outnumber them. Popular notions aside, cats rarely attack rats, though rodents do avoid nesting near often-pungent cat colonies.