It takes approximately 80mg of copperhead venom to kill a man. An average adult copperhead can inject 40mg. They would be capable of killing a hen based on that alone. A baby copperhead would not be likely to kill a hen. There fangs are small, and they do not put out a lot of venom.
A chicken would be hard to get an effective bite on, that is through all of that feather. A bite to the face would be the worst possible scenario for a chicken. An example would be if the chicken went face to face with one.
Copperheads are shy retiring creatures. They are not particularly likely to hang out in an active chicken coop. That is not saying that one will not pass through. They just are not like rat snakes where they would actively search a chicken house looking for eggs and young birds. Rat snakes are bird and egg eaters. They are nest robbers by nature.
All of that said, the likelihood of death by copperhead for a chicken is slim. Not impossible, but not likely. A hen molesting a copperhead could take a face bite. If you suspected a snake bite from a copperhead, you would not be looking for fang marks on a dead bird. You would be looking for excessive swelling, discolored skin, and giant blood blisters called blebs. You would see the injury before the bird died. A copperhead bite will not kill an animal the size of a hen fast. It will take time.
The venom from a copperhead is hemotoxic. The enzymes will start breaking down tissue and causing internal bleeding (similar to what you would see on the surface with the blebs). These symptoms would progress over a period of time and you would definitely know something was wrong with your bird first. Maybe if the bird was bit at dusk, you might find them dead by the morning, but even then it would not be hard to find the symptoms and damage from the snake bite. It is not pretty and it is unmistakable. It is also very very painful.
Trust me. I have had been bitten a few times myself.
