I think with early socialization and training, it may be possible. Personally I would stay away from field labs, they tend to be more "high drive" and retrieving birds is very natural to them. It doesn't matter if they are dead or alive....they want to retrieve them, that is what they do.
Don't forget if you ask a breeder of labs "how are they around birds/ducks", normally an answer of "good or great" means they are very interested and would love to kill them or carry them around.
I could never have free range ducks or geese around my labs, but mine have already had the "taste of feathers", and they hunt/retrieve regularly.
Personally I would look for a different breed, you may end up having problems. Labs were bred to retrieve game, that is like putting a steak in front of a starving man, and expecting him not to eat it.
I am sure there are some labs that would have no interest in your chickens and ducks, but I think that would not be the norm.
I guess it just really depends on the dog, and how you would train him.
Good Luck!