Since you are restoring to the same device, see http://support.apple.com/kb/ht4946
Managed Configurations/Profiles. When restoring a backup to a different device, all settings related to the configuration profiles will not be restored (accounts, restrictions, or anything else that can be specified through a configuration profile). Note that accounts and settings that are not associated with a configuration profile will still be restored.
The profile would be included in the backup. If you restore the backup the profile will come back. If you don't want to restore the backup for troubleshooting reasons, just have the profile re-added by whoever put it on.