Sure, assuming you somehow figured out projective geometry you could figure out what was casting the shadows. That doesn't contradict Plato, because that's what he thought philosophy was. Compare what the invention of the calculus did for physics. The real numbers can't be seen, observed, and do not affect the physical world in any shape or way. Real analysis is pretty import all the same. Objects not existing in that sense doesn't necessarily mean they're not worth studying. There are a lot of problems with Plato's metaphysics, and Plato himself pointed out the more glaring ones (see Parmenides ), but this is not one of them.If you were in a cave you could likely, with enough time, through looking at the shadows, learn that they are shadows.
The question, I guess, is "is there a reality beyond ours we don't know about". Honestly, it doesn't really matter. It apparently can't be seen, observed, and doesn't appear to effect our physical world in any shape or way, so it may as well not exist, even if it does.