Yes but you need a Streaming audio recorder. Can capture and record only the music being streamed through your browser so any other sounds are ignored from the start.
Actually I am using a soft called Audials Tunebite to record online streaming musics.It works with Napster streaming website very good and I see that they even have a tutorial about how you can record music from Napster: http://audials.com/en/how_to_record_internet_radios/napster.html
Hope it helps!