There is a plugin for the Wii U plugin system to stream one of the screens to the PC, it might only be the gamepad screen as i recall. But I'm telling you straight up, the quality is terrible. Like the framerate is solid as I recall, but the resolution is terrible.
I suppose it is an OK solution to use hand in hand with a capture card so you can capture both screens, have the lesser quality Gamepad screen much smaller in your stream with the main screen taking up the most of the screen (like when people stream DS or 3DS) and that would be probably the most effective way to capture both screens for streaming.