By great quantities I would say they fill their crop as soon as it is dumped. I actually checked crops before and after one time.
They are on 20% grower as an all flock. I also scatter oat, wheat, peas, milo, boss, millet, milo over their range to encourage them to spread out and forage. Insects are plenty during the warmer months. I keep a whole bale of fine textured alfalfa under cover for them to nibble as they please. I think the only thing lacking is live greens.
I agree that the probiotic benefit of the manure could well be the motivator as the probiotics would make it a live green food of a sort.
I do not get the filling the crop part. I get eating some, and scratching through it for other things. I do not get living off of it. But whatever they are craving, they will get enough of, and a balance will return. They will probably still eat some, but in moderation. They instinctively find a balance, and they have had said that something is missing. LOL.
Cheap feed I guess.