I've actually done this thing, as in I've participated in a 10-day Vipassana meditation course, during which participants cannot listen to music or interact with each other.

I can say that forcing silence upon myself resulted in a "mental withdrawal", if you will. It wasn't very pleasant, the music gets louder and louder and quite unbearable at times. That said, I did indeed see some effects at the end, in a form of periods of silence in my mind(which was kind of spectacular for me; there's some music in the back of my head at all times). My opinion is that even longer period of non-listening would yield even bigger results.

I really recommend the experience(the deprivation, I mean; the Vipassana part is also cool, but kind of orthogonal). Even though it's very demanding, you can really put things into perspective and learn a lot about how your body reacts to things. It also gives you a completely different outlook on stuff like solitary confinement.