The Wii U sends the signal directly to the GamePad and it has almost no lag (less than usual televisions). It isn't designed to be used it in the entire house. It works with a very high bandwidth, the video stream that is sent to the GamePad has up to 40 Mbps and the audio is uncompressed.
I would love to use the GAmepad around the entire house??? Ins't this bad news???
But, then how can you play such games as Batman & ZombiU & Nintendo Land & etc. if you don't have the GamePad near the TV to interact & work with one another.