I think it really depends on whether the neurons responsible for handling vision processing have any natural spatial processing ability. It's not obvious to me

I think it really depends on whether the neurons responsible for handling vision processing have any natural spatial processing ability. It's not obvious to me whether they would or not. My guess is that allowing some time to look around the objects (without being told which is which and without touching them), that they would be able to create spatial relationships for vision processing (sensorimotor loop) and be able to overcome this issue. Once there is some spatial reasoning for the two different types of input, I believe they would begin to build correlations between them (only for very simple shapes). Perhaps an experiment could be made that would answer this by giving a person a completely new sense and asking the same identification problem. I think the skin could be interesting to use as it allows 2D input with the possibility of utilizing existing spatial mapping, yet isn't used (in most cases) for 2D depth feedback. You could attach some device that heats/cools, pokes, pinches or something else to excite nerves based on some depth information. Of course they would be blindfolded and unable to touch the objects. You could make two different types of experiment, one that has spatial mapping to the skin and another that is randomly linked, seeing how long (if at all) it takes for somebody to figure out from the inputs which shape they are observing. My guess is that they could quickly get an intuition for each shape simply by looking at the rate of change of inputs when they move about the object.