While implementing Intune at my customers I rarely encounter green field implementations where computers and mobile devices are newly delivered and no data needs to be restored on the device. Most of the time, the devices are already in use and we need to figure out some strategy to deal with the data from the device, before we re-install the device and bring it under management.
For iOS devices I recently did some testing about the possiblities of restoring iTunes backup to devices which are re-enrolled into Intune, therefore receiving a Management Profile.
Outcome
When we create a backup of an iPhone with iTunes, reset the iPhone and do a re-enrollment and during that process choose to restore the backup created, we end up with an iPhone having a restore from the backup but without an Management Profile.
If we create a backup on iPhone A though, run the same procedure on iPhone B then the backup gets restored, but the Management Profile is retained.
Conclusion
If you want to restore user data from an iTunes backup on iOS devices during re-enrollment of the device in order to include it into Intune management, you need to restore that backup to another iOS device in order for the Management Profile to retain on the device.