Finally, a concrete answer
With all of the good news rolling in on Hyrule Warriors, this new information comes with a fair bit of disappointment -- there will not be online co-op for the game's campaign. Confirmed on the official Japanese Twitter account, local play will be the only option available for the full story mode, albeit with a split GamePad/TV situation to accommodate more screen real estate. Some form of online play is confirmed, but we don't know what it is yet -- it sounds like a minigame.
This is a pretty big disappointment, since recent Dynasty Warrior games -- heck, even the portable versions -- have online story mode play. Nintendo has always been kind of behind in that department in terms of their consoles, but the Wii U has stepped things up considerably. Just...not in this case.