Even with the admin account, Windows still needs to launch UAC:
https://learn.microsoft.com/en-us/windows/security/application-security/application-control/user-account-control/how-it-works
"A user that is a member of the Administrators group can sign in, browse the Web, and read e-mail while using a standard user access token. When the administrator needs to perform a task that requires the administrator access token, Windows automatically prompts the user for approval. This prompt is called an elevation prompt, and its behavior can be configured via policy or registry."
installer.hasAdminRights() is true only when the UAC has been accepted. Unfortunately I don't have a solution for you to differentiate between normal and admin user. Windows does not seem to have a registry value for it either which script could utilize.
Even with the UAC accepted, connection to the repository and download should be possible. Please file a report about this with details to https://qt-project.atlassian.net if it is not working for you