Yes...but I bet at least 60-80% of the games won't use the extra screen for something that really REQUIRES a second screen (including all the multiplatform games). In fact, I think more than a few third party titles will offer the option to not use the extra screen (if not because it's counterintuitive for gamers to check the two screens at once, then to save battery life).
So in the end, I think the option to continue playing on the controller screen is exactly because nintendo expects/anticipates that the extra screen won't be the next revolution in gaming. By allowing developers to keep everything on one screen AND to play on the handheld screen, it'll be pretty hard to claim that the extra screen won't be used.
Well "require a screen" as in actually needing it or "requiring a screen" to map a menu to?
No offense, but I don't see myself paying like $300 (or however much it costs) for a new console that plays basically the same games as my other consoles, but I get to touch my menus now. I mean it's just a menu, unless it's some game which doesn't pause during menus (like I think Dark Souls does this but it's not coming to the Wii U anyway so who gives a shit), I won't find myself really needing a touchscreen menu.