I was researching the Deep Litter Method a bit more today. I hadn't ever heard of Stall Dry until this Topic. Called my Feed Store and found out that it is simply Diatomacious Earth and Volcanic Clay. So it is the perfect dusting combination for chickens I think. On top of that, it absorbs 2 1/2 times it's weight in liquid. So using it with the DL method would give you basically a dry and odor free coop.
The fluffing would bring in lots of oxygen that would keep the urine from becoming ammonia. But another thought is to remember that ammonia is a disinfectant and is what some of us use to clean our kitchens, bathrooms..... So, how dirty can that be.
As long as the chickens didn't have too much of a meat diet, I can't see why the droppings would be any more of a problem than cow patties.... Which when dry are in fact not really that dirty of a material. Simply fermented grass and vegetable matter unless you are feeding the cows something other than their normal diet. The chicken coop would likely be cleaner than what most of us have on the bottom of our shoes when we return home after a day at the "office".
On top of that, there shouldn't be much scraping to muck-out the coop every few months to a year. The only way things would become caked on is if the litter wasn't turned regularly to keep it fresh.
This all seems perfectly natural, and a great way to keep a healthy organic flock.