Same experience as Paul the Original. 

My first drone was a Phantom P3 with a GoPro branded camera attached to the gimbal. The GoPro had a microphone. It really didn't matter how close you were to the noise source, all you could hear was the whine of the props & motors.

I'd think the only way you could get the true sound from the subject is with a remote microphone & separate recording device, then dub the audio to the video in appropriate software. I'm guessing it would be more work than you want. "Keying" sound to a particular moment can be challenging.

After that original P3, none of the drones have bothered to capture audio any longer and that's just fine with me.