Dan,
After all that I realized I did not answer your question..."can you keep your eyes on TV while touch typing on the chromebook?"
Yes, and you can bypass the chromebook and make the TV your main screen, however, I have my TV mounted a bit high to make this a bit difficult to do for long periods of time. So if you want the big screen TV as your main screen, I would mount it lower than I did. However, my intention is to have the patient follow along as I chart in room, so mounted the TV at the most desirable height to achieve this effect.