It's advised to spray plants with neem in the evening so that you aren't at risk of spraying pollinators. Directly spraying them will kill them, but any spray residue on the plant at the recommended dosage won't hurt them.
http://www.discoverneem.com/neem-bees-beneficial-insects.html
Pure neem oil degrades quickly in the sunlight or rain so I doubt there will be any left on the greens by the time your chickens actually eat it. Interestingly, I know finch breeders will brew up neem leaf tea as a medicine and to treat air sac mites.