Any user configuration items, including login scripts are run with the user's permissions. In order to run a script (or software installation) with elevated permissions you need to either run it using Computer configuration, which will run as local system, or use group policy preferences to create a scheduled task and configure the desired credentials.
I was able to make it work by putting the script inside the path (inside the GPO):
Computer Configuration\Policies\Windows Settings\Scripts (Startup/Shutdown)
In it, the script runs as administrator by the system, doing the installation.
Hope this information can help you
Best wishes
Vicky