Drones of the US Military type fly very high and are thus quite difficult to shoot down, especially if they have anti-missile missiles (I doubt any currently do as they are only used in battlefields where the enemy doesn't have good missiles).
Quadrocopters could certainly be shot down by robots, but probably not by humans once they get fast enough at flipping themselves around and making evasive maneuvers.
Anti missile defense other than jamming and decoys do not exist for airborne platforms.
US drones operate in an uncontested environment let them try fly over Russian or Chinese airspace, the soviet shot down a bloody U2 thy can hit a globalhawk or a reaper.
HARM is typically used to engage a SAM site's radar, not the SAMs themselves. Intercepting a missile is a bit harder than nailing a stationary emitter. Plus, many SAMs use IR sensors, so if you don't detect the launch signature, it's hard to take defensive actions. DIRCM, laser based dazzlers etc can help, but not if you don't detect the launch.
Quadrocopters could certainly be shot down by robots, but probably not by humans once they get fast enough at flipping themselves around and making evasive maneuvers.