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PATRICK?!?!?!?!? HELOOOOO?!?!? ARE YOU HEARING THIS??!?!?!?!
Hmmm? What? Did you say something?
Oh. Right. Well, yes, it could be done. Much like you suggest, although a quick think-through suggests that you would need some form of feedback to allow precise positioning of the steering, since the little RC cars are not all that likely to run straight.
Bluetooth control as suggested would also be doable, as the cost of bluetooth transceivers has dropped dramatically over recent months. Some of the new modules are cheap, very tiny, and quite low power.
Another possibility for control would be via a PC of some sort equipped with a webcam. Draw on paper, show it to the camera, and the car follows the pattern.
If you wanted to draw on the car directly, you could implement a very small graphics tablet on it, which normally work electromagnetically, using quite simple circuitry (although fairly clever software) and an x-y grid of PCB traces.
OK, how about this? Some small accelerometers and gyros in the car, along with a reasonable processor. Pick up the car, put it in learn mode, move it around, and it memorises the route. Put it down and hit go, and it retraces the pattern. Add bluetooth, teach one, and make a whole swarm move in synchronism 
Or put a solar cell on the top, add a transparent resistive touchpanel, and you can both draw on it and have it power the thing.
So, yer, the concept is possible. Whether you could make it so cheap Mattel could sell it I'm not sure, although quantity manufacture in the far east is pretty effective at making high tech cheap.
The real problem I can see is that these poeple might get annoyed if someone else makes the thing. Also one would need some form of financial backing.
pca
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Experience is what you get just after it would have helped...