How to supervise an unsupervised iOS device keeping the users Data?
According to this discussion thread, you can try the following method:

WARNING: I have not tested this and you may lose data!


  
  Disable "Find my iPad” on the old iOS device, perform iCloud backup on the same device
  Plug in the new device to Apple Configurator, Supervise and update the device to the latest iOS
  Once Supervised, unplug the new device and go through the Setup Assistant to restore from iCloud
  When the iCloud restore of the new device is complete, do not touch the Setup Assistant, plug it back into Configurator
  Before you refresh, change the "Restore" and "Update iOS" options to "Do not Update/Restore"
  Once refreshed, proceed through the Setup Assistant, your device should now be Supervised and ready for MDM Enrollment
  


Note that this is for cloning a device, I have not found a way to use the backup of the same device to supervise it.

Also, it does appear that you can try this with an iTunes backup as well if you'd like. Just follow the same steps and use iTunes instead of iCloud to get a more complete backup.

It looks, however, like some versions of Apple Configurator do and do not work, so your mileage may vary.