Translation:They like listening to music, however they do not listen to pop music.
No, it would sound unnatural. You would only use "the" if you were saying something like "Do you like the music? (but only in reference to music that is currently playing, otherwise, as a general question, you would say "Do you like music?") or "Listen to the music!" (as more of a command and also in reference to music that is currently playing).