“Check for updates” button will be visible in G-C-C (GNOME Control Center) only if you have installed GNOME Software or “gpk-update-viewer” which is part of “gnome-packagekit-updater” package -the PackageKit UI; the predecessor of gSoftware.
The patch came from Antoine Jacoutot and Bastien Nocera pushed it on master.
info: Conditionally display the “Check for updates” button
When neither gnome-software nor gpk-update-viewer are available, it does not make sense to display the “Check for updates” button.
Bastien Nocera #727819
Not something important but it shows the efforts of GNOME to respect other desktops & more distros, on upstream level. Even in the very core GNOME Modules there are many guards to check if they are running outside of GNOME, e.g Ubuntu.