Very interesting question Skye.
I have talked about that subject with a friend of mine. He told me that he knows a guy that works with him that only sees with one eye...and he has trouble with distances and depth (he was born seeing with one eye only). That points to think that he only sees kind of flat images.
But some people who were born with both eyes and then lost one, they can somehow see still a 3-D world...probably their brains has "storage" previous information for them to use later, even with one eye.
It's a complicated subject.
For 3-D Digital Cinema and most TV 3-D display systems, we need 3-D glasses with different sets of filters (polarizer, or colors for anaglyph). Also there are the alternate system of 3-D Shutter Glasses. With all current systems, those 2 sources have to go to 2 different eyes.
Probably if somebody invents a Shutter Glasses system similar to the one used by Real-D that "flashes" both images alternatively, that could solve that problem.
Cambridge Wisconsin, USA.