I wouldn't put it in the coop as you wouldn't want to bring in any possible pests into the coop. Plus as they dry they might make it a little more dusty than you would want in there, I think--this is a guess.
I do put in some raked leaves in the run in a pile which allows the chickens to find some tasty bugs, have some entertainment and then they mix it in with the rest of their run materials (we have wood chips, ash, dirt and some straw the chickens kick out of the coop). I would make sure that they are really dry otherwise you might run into some rotting which would cause some un-needed smell and/or freezing (or mold in earlier autumn).
They say a mix of materials works best for deep litter in the run
I used to pick bags of leaves off the curb in town. I piled leaves 3’ deep in the coop and run. The hens tunneled in the leaves, scratched them to bits, pooped on them and in a few months time reduced the leaves to a fine black crumble. Garden gold.
YES! Leaves make great deep litter!
I tried leaves one time and the ducks didn't like them, in the barn anyway, and avoided sleeping on them. Chickens didn't mind either way, since they roost.
It seems like pine shavings are more absorbent than leaves, and the poo messes stay on top of the shavings better and easier to clean up that way.
I would totally use leaves. Now that we have a lawn sweeper, I’m hoping it will be a lot easier to collect them.
I also use pine needles from under my pine trees, and grass clippings.
Anything you can find free on your property lowers the cost of the pine shavings you have to buy. I use some pine shavings, but they are my least favorite because they make big matts.