Only if you tell it to.

In the Options dialog, if the checkbox "Delete Favorite Places / Bookmarks" is checked, then next time you run CleanUp! it will delete you favorites and bookmarks. To help prevent you from accidentally checking this, CleanUp! 2.0 and later includes a warning message as a reminder.

Note that once you delete them, there is (deliberately!) no easy way to get them back! Generally, you only want to use this option on something like a work laptop computer that you are handing back to your employer. You really don't want them to find out your favorite places, do you?