Do I need Directory Synchronization if after migrating a set of users to Target domain I disabled them on Source domain?

Directory Sync is used to sync changes from the source to target after a migration job has been done.  It's also used to mailbox-enable the target objects for an Exchange Migration.  So if the objects are now being managed in the target and no changes are being made to the source objects then most likely you do not need to have directory synchronization running.  

Directory Sync is used to sync changes from the source to target after a migration job has been done.  It's also used to mailbox-enable the target objects for an Exchange Migration.  So if the objects are now being managed in the target and no changes are being made to the source objects then most likely you do not need to have directory synchronization running.  

Once I have migrated all users to Target Domain, there will be Application servers left in the Source Domain, do I need Dir sync to replicate the source Application groups to Target Domain? 

Thank you,