I think it's the other way around, as well. Being a musician makes you a better audiophile.
As an audiophile only, you don't have a frame of reference to compare sound quality. You might like something that sounds really unnatural.
But a musician will compare gear against personal experience. The converse is not true. If you like a pair of colored headphones and then start playing the bassoon, you're not going to think, "hey this bassoon sounds wrong." You're going to realize that your headphones don't sound like real life.
Also, being a musician gives you a deeper understanding and appreciation of music. You will pick up a bit of music theory and an understanding of composition when you play an instrument. If you're fortunate enough to have a good teacher who explains the music as well as the company of other players to learn from, your understanding of music will soar.
Sitting around listening to gear teaches you almost nothing.
So if you want to improve your appreciation of music and get some insight into which headphones sound natural and which sound colored, start playing an instrument. It'll make you a much better audiophile.