I'm not aware of any macOS update which has ever required input outside a user account. The update will proceed correctly regardless of whether you do this, however you won't be able to see the progress of the update, as other sessions are disconnected immediately.
If, on connecting, you get a message that another user is logged in and whether you want to share session or create a new session, cancel and log in as the correct user. Using macOS screen sharing app, connect as an administrator and be the only user logged in to the machine at the moment.
I've tested this by screen sharing a VM and it seems to work great!
