I think it's pretty reasonable to assume that Zelda U, which for most of its development was a Wii U, would make use of the GamePad in some capacity like most of Nintendo's first party output on Wii U has.
Nintendo has been pretty consistent in maintaining backwards compatibility in its consoles over the past decade so assuming that the NX has BC for Wii U games, it's reasonable to assume that it has some kind of second screen controller. Especially so considering that it's difficult to buy a GamePad separately. Wii U had Wii BC but it required you to buy a Wiimote separately for most games. This can't really happen with NX since (I believe) GamePads are not sold separately.
It could be the case that the GamePad functionality in Zelda U is rather minimal though (more Mario 3d World, Pikmin 3, less Star Fox Zero) and so it could be easily ported to NX even if it doesn't have a second screen. This is the most likely scenario in my mind.
An interesting thing to spin out of this thought is wondering how Nintendo plans to handle BC and Virtual Console releases of Wii and Wii U games going forward. A lot of games such as Skyward Sword are unplayable without Wiimote motion controls. Will all Nintendo consoles moving forward have to be compatible with Wiimotes if they want to be able to emulate Wii games?