I always say, anything is possible, the question is whether or not you want to spend the time that it will take to achieve it. However, I think you could do this without too much trouble by using two different views and a little bit of code behind your button. To provide one-click printing functionality I would do this:
1. Place the button on the text data view.
2. Place code behind the button that prints the current view, switches to the drawing view and then prints it.
The bad thing is that you must use full trust if you want to call the PrintOut() method for printing. To setup page size and orientation open the View Settings dialog box by double-clicking the view in the Views task pane.
I hope this helps!
Matt Faus / Microsoft InfoPath MVPQdabra® Software / Streamline data gathering to turn process into knowledge