It seems to me that the application was designed to INTENTIONALLY use the users AppData folder to store its settings. It's generally a bad idea to mess with how a program was designed to operate.
HOWEVER, if you have the ability to run a different program that can do file syncing between different machines on the network, you can certainly do something like make a single copy of the config file and put it into a folder somewhere on the network - preferably on a file server, then use a file syncing program and set it up to take that one file and copy it out to each users workstation and drop it into that AppData folder.
Then, you would only need to make a change to that one file and the file sync software will see that it was changed, then it will copy the new file out to the users' workstations.
Here is a link to a site that reviews a bunch of different Windows programs that do file synchronization ... there are probably thousands of options out there ... just google around and find something that works for you in your environment.
By the way, if you go this route, I would make sure that any time you change the config file so that it copies out to the user's workstations, that the users shut down the program until the file has been copied to their workstation. It's possible that the software could have open locks on the file or that changing it while the software is running might piss it off ... so it's just good measure to shut the programs down, then sync the file then have them launch the program again.