I suspect the birds would eventually ignore the drones unless the drones are made to pose an actual physical threat to them. City pigeons are so accustomed to cars and humans that they barely move out of the way in time to avoid being crushed.
Well sheep have been herded by dogs for millennia and I think it's pretty rare that they actually hurt any sheep.
Come to think of it, birds don't even make enough of an effort to avoid existing aircraft that are large, loud, and do pose a threat to them, which is why these drones are being developed in the first place.