$600 wouldn't even cover the cost of an autostereoscopic 3D display; defintely not a 24" one.
A 24" version of the same type of Sharp manufactured autostereoscopic display used in the 3DS wouldn't be ideal either due to its parallax barrier, which would only make it suitable for single player desktop use. Desktop use and motion controls don't exactly go hand in hand.
But all that aside, since this is just a hypothetical "wouldn't it be cool" post and mock up: I would definitely pay $600 for the product described in the OP if the display had a video input of some kind (which it probably would for plugging in an external video source for watching movies).
I would buy one just for the 3D display alone to be used as a computer monitor or as a display to watch BD 3D movies at my desk.
It would be a bargain even without the console inside the display.
And no, Nintendo would never sell something like this because they would have to charge Apple prices to make it profitable which would make the price tag considerably more than the lowball price suggested in the OP.
For reference, Sharp's LL-151D 3D autostereoscopic display (15" 1024x768) costs about $500 as of last year, so do the math.