It doesn't seem to check for updates.
I think it's gnome-packagekit that's being used.
My system is:
System: Host: jaa-debian Kernel: 3.16.0-4-amd64 x86_64 (64 bit)
Desktop: Cinnamon 2.2.16 Distro: Debian GNU/Linux 8
I've tried to find the "Software Update Preferences", but haven't found it. The manual says:
Preferences can be configured via System ▸ Preferences ▸ System ▸ Software Updates.