If you installed the Stand-Alone Addon Manager, you wouldn't need the Live Update anymore, because installing the Stand-Alone Addon Manager does the SAME (and more) as installing the latest Live Update.
If the Stand-Alone Addon Manager didn't show any errors while it installed and downloaded files, it means the Live Update server was running normally, because it's the same the Addon Manager installer downloads from. In fact, there are two mirrored servers, so it's unlikely the server would normally ever appear to be down, unless some kind of security software, like a firewall or an antivirus, is blocking the Live Update from within FSX.