1st question is which profile?
If they are using ‘Roaming Profiles’ to logon so they can use different workstations, then yes you can delete the local profile as part of logoff/shutdown – GPO entry.
2nd – If you are referring to the ‘profile’ saved on the server – why?
3rd the reason for local copy of the profile is to reduce the login time that results from not having saved personal settings locally. If it is security that causes the need to delete the locally saved copy, then monitor the profiles closely. Two or three documents saved to the desktop, a hundred megs or mp3’s in %user%music% and login time are greatly extended.