A) If the music was obtained from someplace other than apple this works (you then allowed apple to use said music for it was in your music library.)
B) If the music was obtained from apple prior to 2009 you may need to reconvert said music to another format. Google Music does this automatically for you for free (and uploads said music online.)
C) If the music was obtained from apple after 2009 what you describe also works.
So in most cases what you are describing works, with part B you can make it work but it requires converting the music which doesn't have to be hard unless you make it so.