Dear Jon,
This is absolutely correct, DocuWare User Sync will 'move' the users for you to a new group. However, this always depends on the actual configuration.
Which User Synchronization are you using? The integrated one in DocuWare Administration, referred to as User Sync V1, or the standalone Desktop App, referred to as V2. See screenshots below:
Best regards,
Thomas Esser
Sr. Specialist Software Support Team RED EMEA