Sometimes well, sometimes not. Bird strikes are relatively rare, but do happen. I've had two. One tiny guy on the wind screen on landing at about 150mph which caused no damage and one on the nacelle of a jet engine at around 270mph that did cause structural damage. I also own a little DJI phantom "drone" and have no doubt that it could snuff out a turbine engine if it was ingested or cause significant structural damage. Unfortunately the FAA can't go after birds with fines for busting class B airspace, but they can and should nail drone operators.
The little copters are really awesome to play with but the FAA needs to start upping the enforcement. You need to be licensed to talk on a ham radio, you should be licensed to fly a drone. Not a full on pilots license, but written tests on airspace every year or two. It would be nice if future drones continuously transmitted the operators credentials on a publicly available frequency.