Yes, the SSL certificate used by the WSUS IIS (update.organization.com) is installed in the Computer account personal store of the WSUS server.
No, the WSUS server itself is not registered in the WSUS as a Client.
Yes, the SSL certificate used by the WSUS IIS (update.organization.com) is installed in the Computer account personal store of the WSUS server.
No, the WSUS server itself is not registered in the WSUS as a Client.