Per:
http://www.ilounge.com/index.php/articles/comments/removing-songs-from-the-clock -alarms-list/
you do not.
It includes saying:
However, this is actually just a listing of the five songs you’ve most recently used with your alarms, so it won’t continue growing indefinitely. When you choose a sixth alarm sound, the oldest entry is pushed off the list, such that it only ever shows the most recent five selections.
Read more at http://www.ilounge.com/index.php/articles/comments/removing-songs-from-the-clock -alarms-list/#XWhzYSJrIqf3uokB.99