In Manage Backup Sets under the WHAT tab I clicked on “Add or exclude files and folders” and added the folder “C:\WINDOWS\” but that folder is never backed up. Is this by design?

Yes, it is true that Norton 360, by design, does not backup system files or whole system drive partitions. Its backup features include backing up data files only, like your documents, photos, movies and anything else that is not part of operating system or other software installation.