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As always there is the disclaimer that there is no predicting what a dinosaur might do but . . .
If your hen is broody, her instincts will be to hatch and then, literally, take the chicks under her wing and provide them with warmth while undertaking an orientation program , introducing them to the world, teaching them what they need to know.
Part of her duty will be to introduce them to the rest of the flock and teach them how to behave as they work their way into the pecking order.
In some cases this may require defending them, not something all broodies will or can do.
So the idea of a dog crate in the coop for the hen and chicks might be a good idea. If you look through the threads about introducing new birds to an existing flock, you'll find a lot folks have had success with letting both the old and the new out to run at the same time for a while with a fence between them. This allows them to at least get used to seeing each other. After some time, they are let out together. As long as there is sufficient room for the bottom birds in the pecking order to get away, they will sort it out. Keeping them crated where the other birds can see the chick is the equivalent of the separately-fenced stage, and may be just the ticket..