If the Wii U had full support from all the major 3rd parties, would it have competed with the PS4?

[Chief]

It couldn't possibly get all current-gen multiplatform games with that hardware. Games like AC: Unity, AC: Syndicate, The Witcher 3, Batman: Arkham Knight, Fallout 4 and Middle-Earth as well as many upcoming current-gen exclusives will not run on Wii U. So it would have sold more, but not much.