I had the same question. Really, these things bug you when you start late. I started at age 16-17. I have been playing for a year and a half only, no formal training, very little playing time evryday(way too much academic work),can't afford a piano(in the third world, a shitty casio is all you get and i dare say i am well off here), largely self-taught, nowhere to buy scores or even recordings(hate to say it but piracy is our only friend here).
With the help of another self-taught guy, i managed to learn fur elise up to the run, bach's minuet in G completely, the entertainer up to the tough part(i dont even know wat a movement is and hence dont feel confident to use the term), a part of the sonate pathetique (by beethoven i guess).
I doodle a lot on the keyboard, play a lot of blues and some jazz(no pieces, just improvisation), try and figure out stuff about composition and try having a good time with it. i pick things up little at a time here and there.
With these difficulties, i struggle to be a musician in a place that won't allow you. And I think it is possible.