Can a standard user upgrade OSX versions or does it have to be an admin user?
In order to make any "deep" changes to macOS it will ask for an Administrator username and password.

The only way a non-admin user can get around this limitation is by knowing the username and password of an admin user.

So no they can't use that app to upgrade their systems.

They could however copy the app off and make a bootable USB installer on another Mac and then boot their work Mac from that USB to upgrade it, depending on how technical they are. or how determined.