My take:
If your dogs are a part of the family and mainly live in the house, have house rules, etc., you'll be able to teach them the chickens are part of the 'pack.'
I brooded my first birds in the house and brought my Lab and Terrier mix into the room with the chicks daily and made them lay down while we spent time socializing with the chicks for an hour. By day 3, the dogs were bored.
We continued this until the birds were ready to go outside- this *DID* change the way the dogs saw them- temporarily.
We never left the birds and dogs unattended together until we were certain the dogs wanted to protect the birds- that was about a week in when a neighborhood cat came around.
I would feel safe leaving my dogs in the coop overnight. It's just the way these dogs are, though. I can tell you it's not a lack of prey drive- the Lab still tries to get squirrels and occasionally gets a tail (but loses his grip). The birds are HIS birds, and he won't mess with them at all. He patiently waits until they walk away from treats to get his share, btw.
I don't want to encourage dangerous behavior- you have to de-sensitize the dog to the birds. I don't actually know if Henry wouldn't eat other chickens- you know, ones that aren't *his* birds. He might!
ETA: Both dogs were over 4 years old when we got birds.