It depends on where you live. Here in south central Texas, the yaupon and scrub oaks were naturally in our large "day spa" run area... And the chickens never eat them. In fact, my husband has to go a couple of times each summer and trim the yaupon back to keep it from getting too big and taking over the run.
And while not good for shade, we had volunteer tomato plants come up in the coop last year... and the chickens left them alone. They did eat the tomatoes but the plants were fine and grew huge - even without any extra water! This year, we're moving some of the little tomato plants to the garden to see how they do being taken care of! They have to be sturdy to be happy surrounded by chickens.
But, if you have local growing shade plants - try those. Yaupon works really well here.
