"Automatic Software Downloads" won't affect the system updates. If your system is in Sleep Mode, and has access to the internet, it will check for a new version. If there is a new version, it will download it. If it downloads it, it will start asking you to update about once per day. ("Access to the internet" includes certain free hotspots, anything set up for SpotPass. This includes most McDonalds and other places, even without any sort of settings saved.)
If you do get the update nag in sysNand, you can remove it by using Restore Mode. With the system off, hold down L+R+A+Up (D-pad) and power on the system. It'll enter a menu that asks you to connect and update, but then you just exit the menu/turn off the system. Entering the menu removes the downloaded update (since the idea is that there was a problem with it, and you need to get a new copy), which causes the nagging to stop. You can't enter the menu in emuNand, though, so if you get the nag in emuNand, you just have to be careful. Keep a backup, and if you accidentally update to something unsupported, restore the backup.