Unless they have an adverse reaction to the Benadryl and it causes them to become agitated and distressed, which is a distinct possibility.
I've often wondered if there should be sticky about this very thing that one could direct people to who are looking into owning chickens. This seems to happen quite frequently on here....sick birds that need the hand of mercy and people who do not have the will, heart, or whatever to do the deed.
It should be stressed to these people, before they ever contemplate getting chickens, that chickens are not exactly like other pets. You may have to kill one to end suffering caused by disease, animal attack or reproductive problems.
It is a part of any responsible pet ownership to be able to care for your animals if they are suffering, be it with vet care or at home. Why is it that so many are unprepared and have no idea how they will handle it when the day actually comes? Is it because that part of this whole forum is like the elephant in the room....no one wants to address the death of these animals except in reference to meat chickens?
I think there should be a sticky with methods of humane killing for people to reference and they should be directed to it when they first start asking questions about owning chickens.