Sure.
The Wii U has the Wii's OS integrated, it's known in Gbatemp as the Virtual Wii or vWii for short.
The original Wii was capable of running GC games natively, this function, of course, is absent on the Wii U for normal users due to the Wii U not reading GC discs and the GC games not being available digitally.
The vWii on the Wii U does have the capability to launch GC games, there's a vWii homebrew that allows the execution of GC game images. I cannot elaborate much since it's technically illegal >.< but to keep it short, the Wii U has the software required to run GC games through it's Wii OS, other features not available physically, like memory cards, can be easily simulated.
So, Ninty doesn't have much of an excuse to not put GC games available as VC