Yes, and other birds, too. There are jays and cowbirds around here. Jays are very happy to eat baby birds in the nest. Cowbirds lay their eggs in other birds' nests, and their chicks hatch first and eat the other chicks.
We have gnatcatchers that nest over our garage door and raise a brood of cowbirds, two years in a row now, before they get to fledge their own brood later in the summer.
Last year a hawk was eating a bird ALIVE in my back yard....