I can personally vouch for spaying and neutering being very important for the health of your entire homestead...
I got to help a neighbor find abd euthanize over 50 cats :( Too many cats, not enough food, health declined, and then a few rabid coons and now he has 2 cats left.
It was horrible...
That's how it goes here, too... Of course they look, but don't touch... Most times I'm yelling at a chicken to leave the poor cat alone ;)
That being said, I still wouldn't leave my cats to "babysit" the chicks without a full grown hen nearby to remind them that they're MY BIRDS, not theirs :D