Using Active Directory with Windows 2003 and Windows XP boxes as clients, is it possible to run a script on start up so no matter where a user logs in at the script will create a desktop short cut automatically on any box to their shared directory on a networked drive?
Sure. There is a setting for the user account in AD called "login script" that is intended just for this. The script should be located in \yourdomain\sysvol and should be written to adjust for the particular user.
As an alternative you could specify the script through a group policy.