If the thin client has Unified Write Filter (UWF) enabled, applications can read and write to the disk normally. Any saved data will be lost on a reboot.
If data needs to be preserved between reboots, you will have to open holes in the filter to allow writes through. For your application, you would have to open holes for the AppData folder, Program Files, etc. The uwfmgr.exe utility can be used to perform this task. The AppData folder will be a challange since it used account dependent.