Yeah, they will eat small birds or other small animals to get needed...Calcium? I've seen small birds pecking around bullet woulds of recently shot deer.
They are usually after protein. When I was in grad school at Texas A&M there was a lot of research being done on deer nutrition by the Wildlife Disease Unit at the vet school. They had a couple of pens full of deer on low-protein diets. The feed they used was pelleted and birds, primarily blackbirds and grackles, would fly into the pens and eat the leavings. Several of the deer learned to stalk and knock the birds down and then eat them.
Protein is often low or even clinically deficient in deer winter forage. Deer actually need carbohydrates for energy worse than they need protein at those times. But if they are starved for protein, they will opportunistically get it when and where they can.