I've had standard baby chicks running around the yard for several years. My broodies have kept the cats in check. I do however, keep the bantams in runs.My cats used to eye my bantam and runt chick drooling with greed. The male cat had a go at them once or twice and the broody stopped him, but I didn't dare leave them on their own when the cats were out in the morning until the chicks were a few weeks old.
I would not trust that things would necessarily work out.
Depending on the cat's size, you could maybe make an entrance small enough for your adults free ranging bantams to get in and out, but not for the cat.
The cats here must not be as aggressive. Although the sure go after the rabbits and squirrels.