Isn't it as simple as changing the updater option under the Edit - Preferences menu?
When I change the updater option under the preferences, it changes a registry value located here:
The value it changes is a DWord value of "iCheck". The three options for the updater were:
"Automatically Install Updates" - iCheck = 3
"Automatically download updates, but let me choose when to install them" - iCheck = 2
"Do not download or install updates automatically" - iCheck = 0
This was on a Windows 7 pc. I can't answer if there are other things going on elsewhere that might have an effect on the auto update function of Adobe Reader.
I do see that Reader X insists on running a few things like past versions when Windows loads.
StringValue - Adobe ARM = "C:\Program Files\Common Files\Adobe\ARM\1.0\AdobeARM.exe"
StringValue - Adobe Reader Speed Launcher = "C:\Program Files\Adobe\Reader 10.0\Reader\Reader_sl.exe"
StringValue - AdobeAAMUpdater-1.0 = "C:\Program Files\Common Files\Adobe\OOBE\PDApp\UWA\UpdaterStartupUtility.exe"
The 'AdobeAAMUpdater-1.0' entry appears to be a new one with ReaderX as I don't recall seeing it in past versions. We normally remove these items from auto starting for our users since none of our users are admins and can't perform an auto update or installation. (Actually we leave these entries here, but we "blank" them out because in past versions every time a tech would update Reader, it would re-write these values which we don't want and we found leaving the entries there, but blanking them out, left them alone if you did a manual update.)