Automatic Updater does not do any backups, but if you a have a backup plugin that can be triggered through a function call, Automatic Updater provides the auto_updater_before_update action, which you can listen for and run your backup when the action is triggered.
http://pento.net/projects/automatic-updater-for-wordpress/
Alternatively, a service like VaultPress can keep your site backed up automatically.
Ok,it seems a bit difficult for me…
If writing your own code to link Automatic Updater to your backup solution is outside of your expertise, then I would strongly recommend VaultPress to take care of it all automatically.
