The Wii used trimmed down GameCube hardware to accomplish GC playback. The Wii U does not have said hardware. Virtual emulation is at best unlikely and on a homebrew level, near, if not completely impossible.
@Xdqwerty, Osu! Tatakae! Ouendan! is the Japanese version of the game, different settings/characters/songs but otherwise identical mechanics. I played that before I knew about Elite Beat Agents lol. Both fantastic games https://en.wikipedia.org/wiki/Osu!_Tatakae!_Ouendan