Yes, radar beams are reflected off swarming masses of birds just like precipitation or water vapor. In the early days of World War II, British radar operators noticed mysterious, ethereal shadows drifting across their screens. In 1958, a New Orleans high school student named Sidney Gauthreaux figured out they were masses of birds.
Next Generation Radar (NEXRAD) made studying bird migration much easier. The Air Force started using it to avoid collisions in their Bird Aircraft Strike Hazard program.
More information available from The Cornell Lab of Ornithology website https://www.allaboutbirds.org.