Yes, we use UEM/DEM to manage application data like that.
The key is getting the data to a location that DEM can reach. if it is a DirectFlex enabled app, you can configure User Environment Settings pre-export and pre-import tasks that copy app data between ProgramData and somewhere DEM can reach (like AppDataLocal). If it is not a DirectFlex-enabled app, you can accomplish the same thing with logon/logoff tasks.
You then set that DEM-reachable path to be captured by DEM in the app's Import / Export settings tab. The user will also need access to both the ProgramData location and the DEM-reachable location, since the tasks run under the user's security context.
As DEM is unable to reach config files that are in illegal places you can do as dolzhenkom suggests, but it's also possible to make a symlink from ProgramDataFolder\Folder to a folder in %APPDATA% so that DEM can manage it.