It looks like the auto update software option only updates the firmware and NSO apps. It didn’t update any of my games and I left it on for a couple weeks and continually logged back into the eShop since it sometimes signs you out after long idle periods. I also disabled sleep. It never updated any games.
However, I found out that if you hit the + key on the game thumbnail, it brings up a menu where you can select to update the software via the Internet. It’s still faster than having to load every game to check. It took me about half an hour to check a few hundred games.