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Yes, a human death from a copperhead would be a rare event. An infection from the bite or dead tissue caused by the bite is the biggest threat. it would not be unusual to lose a finger, thumb, toe , etc. as a result of a bite. Still not likely. It is not that their venom is less virulent than some it is a matter of quantity injected. It would take about 80mg of copperhead venom to kill the average man. They are not likely to inject more than 40mg (and that is a decent sized copperhead). For comparison it would take a similar amount of Eastern Diamondback venom to kill a man, but a big one is capable of injecting more than 400mg.
It is still not a bite to take likely. I have been envenomated by a copperhead three times. One of these bites was a pretty good one, and I promise it was a hugely painful experience. It is not an experience that you will ever forget.
On another note, I would be surprised to see evidence of a copperhead invading a chicken house to steal chicks. That is just not their thing. They are ambush predators that prefer to remain concealed where prey is likely. They are more likely to take up residence in your wood piles, debris etc. and hang out. They aren't big climbers either.