Hi Peter,
The Adobe Application Manager was being used before Creative Cloud but just wasn't directly accessible to users. It is used for installing updates for both retail and subscription products. The desktop shortcut can be removed (just the shortcut itself) as Help > Updates can still be used to initiate it without the shortcut. It doesn't have a separate uninstaller in Programs and Features because it is required for all CS6 products. When you uninstall all CS6 apps it gets uninstalled automatically. It works similar to Bridge CS6 (gets installed/uninstalled along with other programs and doesn't have a separate way to be removed individually).
Technically it is possible to remove the Adobe Application Manager by itself using the Adobe cleaner tool, but this would only be needed in edge case scenarios, like it was damaged or didn't install correctly, as it would still get reinstalled automatically when applying updates.
Hope that helps,
-Dave