Is listen-hear parallel with read-understand?

I would phrase the analogy

READ : UNDERSTAND :: LISTEN : APPRECIATE

where appreciate is used in the sense

"To apprehend or understand clearly or correctly; to recognize or grasp the significance or subtleties of." (from the OED Online, 3.a)

As such, I don't think your statement is accurate--many people listen to various forms of music without appreciating it in this sense (and also without appreciating it in the more common sense of liking it); thus "music appreciation" classes.

I think what you're going for is something more like

One must learn to recognize and read writing, but a recognition of music is instinctual.

or perhaps

One can look at writing without reading it, but it is impossible to hear music without perceiving it.

You are probably aware that there is some debate among psychologists about whether music is instinctive or learned or something in between (thus my use of "instinctual" above), which might make the latter a safer choice.

Edited to add that if it is the physical properties you are most interested in, you might say something like

One can close one's eyes to writing, but one cannot close one's ears to music.