You can do the update process, browse the internet and MiiVerse, and run many games on just the GamePad. The worry about the update process only applies to the time when you're installing the update, not while it's downloading. However, keep in mind that the GamePad range is pretty poor, so it may not work from another room/floor, especially if you can't even get Wi-Fi, which has far better range. And it occasionally desyncs with the console, meaning you'll have to get over there to reset it.