WD My Book 2TB External USB 3.0 HD

Will this work with the WiiU?

Not in this capacity … as it appears that the WiiU can only support 2TB HDD. See this link …
http://en-americas-support.nintendo.com/app/answers/detail/a_id/1359/~/what-external-storage-devices-can-be-used-with-wii-u%3F