Just reiterating some of the points above:
- No need to mulch, the chickens will break down the leaves for you.
- They're great in a run, but not as the only component, because once they get wet, they'll compact down and get slimy/slippery, plus they actually break down too fast to be effective for long. Dried leaves with wood chips and garden trimmings will give you a much better result, especially dealing with mud.
I personally would not use them in the coop, but you may have different results depending on your coop set up. If the coop has a dirt floor, I would not use leaves... you end up with the same issue as noted for the run (compact, slimy, slippery) but it'll be even less likely to ever dry out and will probably start to stink over time.
If the coop is off the ground or has a solid floor, leaves *might* work, but you likely will have to change them out faster than other forms of litter, as they simply break down too quickly.