Yes, it is true that young poke leaves are edible for people. I haven't eaten them but have friends that do. I too have read that the mature leaves are toxic to people, at least in large quantities. The berries are toxic to people, as far as I know, but definitely not to wild birds. Therefore, I think it is unlikely that the berries are toxic to chickens, but I don't know about the leaves and stems.
As for putting any part of the plant in a coop of mostly confined chickens, I would first see what they do with it when not confined. The problem with giving treats to confined birds is that they might eat a lot of it simply because they have few other options. Thus, the bird might consume a large quantity of a food that is safe for them only in small quantities.
When my birds are confined, I have no problem giving them berry laden branches of elderberry or autumn olive, because I know these are preferred foods when they are free ranging (I've seen them run over to the shrubs and gobble up loads of the berries as soon as I let them out). However, I don't have much pokeweed where my birds range, have not yet seen them eat it, so I am not sure how much they like the berries or leaves.