No, I don't add mushrooms of any sort to the food I supply. But I have seen the chickens eating some that grow in the garden. I'm not sure how they assess them, but commonly I find the caps knocked off; I don't know if that's deliberate, or if it's just collateral damage of their general foraging behaviour.
I believe the coccidiostat action all happens in the mycelium, not the fruiting bodies. The bit we get to see above ground is just a tiny fraction of a fungus, most of which lives in the top few inches of the soil and may be more extensive than we'd ever guess. The fruiting body is usually nutritious though - lots of vitamins and minerals in a bioavailable form - so if you want to offer them to your chickens, and the chickens can choose whether or not to eat them, I can't see any issue with it.