Can automated web drivers authenticate google calendar signin?

No, you can’t.

See

Google prohibits us from automating UI interaction with Google using any Selenium-based UI automation tools like Katalon Studio. Nobody can cheat Google.

You should abandon this idea as Google will never let you do it.

If you want to confirm that the meeting has been successfully scheduled, your server-side business app should be able to communicate with Google Calendar and test the scheduled result somehow.