I select update and get a message screen asking to leave FSX and obvtain the update. I click OK and that is the last indication I get of anything.
If you see a message telling you to quit from FSX to apply it, it's what is called in the GSX manual a "Major Update" and it's doesn't "just" say to quit FSX, it also says to DOWNLOAD the latest version of the Stand-Alone Addon Manager and INSTALL IT so, of course, the installation feedback is made by that installer. If you don't do that, nothing will happen.
Instead, if the message doesn't say you must exit from FSX, it's a "Minor Update", and that can be applied without exiting from FSX, and in that case you'll see another installer running (if you agree to the update, of course), and GSX would restart automatically when it's done, without having to restart FSX.