My Dad's deer hunting partner had a reloading press inside a shed on his property, which, in addition to reloading ammunition, he raised chickens on. One day, when I was watching him reload shotgun ammunition, he told me "watch this". He allowed a lead pellet to roll off the edge of the bench, where a hen promptly ran over and picked it up, and then spat it out on the ground.
Ever since that demonstration, I've had serious doubts about any birds injesting lead shot.

Best,
Ted