Given that magic eye pictures are basically a certain convolution of a repetitive source image (or random noise) and a depth map, it ought to be possible for an AI, if not a standard procedural algorithm, to at least attempt to "factor out" the source and map from the result image.
Whether that even counts as seeing and whether this guy's neural network could do this, or maybe "see" in some other way is open to question. But I'm guessing it's a no.
I'm absolutely certain you could train them on that.
I stood outside the art place at the beach for three or four hours one day when I was bored helping people see them.
I believe anybody with reasonably corrected binocular vision can be taught to see them.
Almost everybody that can't do it is trying entirely too hard. They're looking for details in the wash instead of letting their eyes uncross and relax. You simply need to use your distance eye crossing while using your reading vision focal points.
Man those things took me years to figure out how to do. It was really hard for me but I finally got it! I have to focus on the image without looking at it directly, and then the image "snaps" into place and I can look at it freely almost. Really bizzare.