I think a small low-res color screen is possible, but I doubt they could use a touch screen without making the controller too expensive. I also don't see much of an advantage to a touch screen, since it would require taking yours eyes off the screen for too long to do anything, and it would require taking your hand off the controller or at least move it a considerable distance.
I could see a small regular screen being useful though, especially if it had two soft buttons and an "ok" button like a cell phone. For instance it could display secret information in a multi-player game, be used to display your inventory (like one of the DS screens often is used for now), and so on.
If the wii2 is using bluetooth it is unlikely that there is enough bandwidth to show live video of any quality. The images would either need to be loaded into the remote's memory early on, or it would need to be small, fairly simple images (like icons) with few colors that can be sent over one-at-a-time when they are needed. On the other hand, if the wii2 ends up using wireless USB instead then the bandwidth would probably be enough to stream live video with the sort of low resolution you would see on such a screen.