I think if you can make that work, it’s an excellent idea.
We used to have outdoor cats, and I used to wish they had access to the coop at night to hunt for mice. (Our cats free ranged 24/7.) But of course, to exclude predators, you have to exclude cats as well. But for kittens that will be locked up at night anyway, that sounds like a great solution.
We had brother cats from a litter in 2009. One lived to be 10.5 and the other to 11.5. They were basically garage cats, and my husband always hated that they walked on his car, sometimes scratched it, and often vomited on it!

So I agreed not to replace them once they were gone.

If I could find a way to have chicken coop cats that didn’t ever go in the garage, I would definitely do it! I miss my kitties.