The Caboose 2.0
I believe the implant description states the user doesn't have to speak, but only subvocalize, which implies the microphone isn't responding to air coming from the mouth but likely vibration directly from the larynx.
I've never used a modern throat microphone, but they operate in a similar manner and one of the advantages is supposed to be transmission clarity in otherwise loud environments.
So assuming the operational principle is the same, and the music isn't so loud and/or at a frequency that is causing Phoenix's internals to vibrate in a completely uncontrolled manner, I figure there should be if not a full reduction in outside aural interference, at least a reduction of some sort.