the chickens will LOVE you for putting it in there, they will scratch through it all the time.
If you do have a muddy run, I would highly recommend getting some scrap pieces of wood to throw down. You could use some pieces as a walkway over that mud, or just put in a smaller 1 foot by 6 inch piece. Every day, or every other day, flip over the wood, and if you are lucky it will be covered with slugs or have earthworms under it. It is SO MUCH FUN to flip it and see the super excited chickens. So there is the benefit of having a muddy run!