All : in fact, getUserMedia isn't usable to do that particular use case.
While you can access the microphone with gUM(), it's not designed to inject the audio flux inside an <audio> object. It's designed to stream it over a connection (like audio caht over WebRTC).
What you need is the Streams W3C API, which no browser support yet.
So, in the end, my C2 webapp can use mp3 or ogg files from the microphone !
That project will be done at the end of the week, I'm going to release the plugin here after that.
Some time in the future, I'll add some JS code to do some basic audio processing on that data...