Specifically is it possible to draw a line on your phone and pass that shape to the screen? Or can I only have buttons on the controller. Thanks!
Your controller is a (mobile) website. That means you can have everything a mobile website can also do such as buttons (touchevent), swipe/gestures functionality (touchmove etc, see e.g. hammer.js), use device motions, camera,...
So if you manage to draw lines on a mobile website, you can also use it for an AirConsole controller. Just keep in mind the latency: drawing lines in realtime on your phone and displaying it on the screen may have some delay. Also sending messages on a touchmove event is a limitation.