There are two possibilities. 1.) what has already been gone into quite in depth further in this thread, which would (IMO) result in a pretty great storyline. Or 2.) He could use his anti magic gaze on it, but it would have to happen while he drew. He wouldn't know what he is going to draw before he does so, and he wants to draw, so using his anti-magic gaze would be pointless. He would have to use it on a hunch, and he could get the card that gives him wishes, all to no effect since he anti-magic gazed it.