Turkeys scratch in the leaves like small velociraptors. You should see a woods after a flock of wild turkeys has gone through looking for acorns. If there is such a thing as a disheveled woods, that's what they accomplish.
I pulled my 25x40 veggie garden last weekend. Added some shavings laced with poo. Left the door wide open and tossed in some cracked corn. No shavings to be seen. They worked it over pretty well for 7 turkeys..
We plan on doing just that: locking the dogs up for a while and putting the turkeys out on the garden with some cracked corn... let's call it turkey-tilling. If they can incorporate the straw and lawn clippings into the garden even half as effectively as they incorporate their bedding straw into the soil of their pen, we'll have some pretty nice soil amendments!