You're probably joking, but that would allow for more run time and also slightly better voice quality since the microphone would be closer to the mouth.
Of course that would be great, but doesn't the brain 'produce' that sound? I'm no medical expert but am wondering if this is theoretically an option. My best guess is probably not.
Your brain produces the sound because, it gets board. Your hearing has holes in it. Frequencies that one or the other of your ears can't hear very well. Because of that, your brain fills in the noise. If you provide just a bit of a tone at that frequency, just loud enough for it to be under your perception, the noise goes away.