Is it possible to deploy the licence file or config settings file from a GPO or InTune?

Yes you can:

ExamWritePad.msi LICENSEKEYFILE="\\Servername\Share\license.lic" SETTINGSFILE="\\Servername\Share\ExamWritePadSettings.json" /qn

Make sure the path to the files is a full path not a relative path:

• Good: "\\zdrive\share\license.lic" 
• Good: "Z:\share\license.lic"
• Wrong: "license.lic"

You can also use GPO or InTune or script it to suit your environment.

To GPO a file you can follow the basic outline from this website:

https://www.techcrafters.com/portal/en/kb/articles/how-to-copy-files-or-folders-to-all-computers-using-gpo#Copyingmoving_all_the_files_into_a_shared_network_folder

To InTune a file you can follow the basic outline from this website:

https://techcommunity.microsoft.com/t5/microsoft-intune/deploy-file-to-intune-enrolled-devices-as-win-32-app/m-p/3855954