@John-Coogan See if you can use a portable installation. The “installed” and “portable” versions are nearly identical. If you download and expand one of the portable .zip or .7z files you will see that the package includes a file named doLocalConf.xml. Delete that file and Notepad++ will use %AppData% for its configuration files. The standard installer copies the files to %ProgramFiles% (64-bit) or %ProgramFiles(x86)% (32-bit) which normally needs administrator rights to copy in the files.
I think the main issue you will run into is that Notepad++ is a project and resulting application designed for individual desktop users. It still seems to be very much a work in progress in terms of setting up an installation for “all users” of a computer, installation on either locked down desktops or remote-desktop machines.
For example, Notepad++'s Run menu allows for the user to run any other application on the machine. You likely don’t want that if you are trying to create locked down desktops for people. Notepad++'s plugin architecture is very powerful in the hands of a person who owns and controls their own desktop but also can be abused by someone trying to bypass controls you may want to impose on a desktop.