If an update has been downloaded and staged, but the user has disabled notifications with sufficient vigor, the update process will be stuck. If the user discovers via external means that the device is behind, and presses the Check for updates button, nothing happens. This is a recurring source of confusion for users (example1 example2 example3 example4).
Multiple approaches are possible, e.g., Check for updates could reenable notifications, or coach the user to do so. But the simplest thing would be to pop up an alert telling the user that rebooting is necessary to install a new release.