Well you don't really need to shoot the Drone.

If I see or hear it coming I know a Prophet is close by and I know I'm not safe I'll reposition myself to where I know I'm safe, let the Drone get me, then press the button to cancel it and kill the following Prophet. Of course it's ideal to not get caught by the Drone but they're pretty easy to trick. The AI in this game is kind of bad, It'll go for the closest target, even if it's chasing another. So you can effectively use your teammates to lose the drone or distract it long enough to destroy it.

Yeah, you'll die sometimes but you can't 100% counter every single thing. You can just make it much more bearable to play against.