In my amateur opinion, it's almost the opposite. For Plato, the material world, while "real" enough, is less important and in some sense less True than the higher immaterial world of Forms or Ideas. The highest, truest, realest world is "above" this one, related to cognition, and (more or less) accessible by reason. We may be in a cave, but all we have to do is walk up into the sunlight — which, by the way, is nothing but a higher and truer form of light than our current firelight. (This idea that material objects partake of their corresponding higher-level Ideas leads to the Third Man paradox: if it is the Form of Man that compasses similar material instances such as Socrates and Achilles, is there then a third... thing... that compasses Socrates, Achilles, and Man itself?)
For Kant, and therefore for Schopenhauer, the visible world is composed merely of objects, which are by definition only mental representations: a world of objects "exists" only in the mind of a subject. If there is a Thing-in-Itself (which even Kant does not doubt, if I recall correctly), it certainly cannot be a mental representation: the nature of the Thing-in-Itself is unknowable (says Kant) but certainly in no way at all like the mere object that appears to our mental processes. (Schopenhauer says the Thing-in-Itself is composed of pure Will, whatever that means.) The realest world is "behind" or "below" the visible one, completely divorced from human reason, and by definition completely inaccessible to any form of cognition (which includes the sensory perception we share with the animals, as well as the reason that belongs to humans alone). The Third Man paradox makes no sense at all for Kant, first because whatever the ineffable Thing-in-Itself is, it certainly won't literally "partake" of any mental concept we might come up with, and secondly because it would be a category error to suppose that any property could be true of both a mental object and a thing-in-itself, which are nothing alike. (The Thing-in-Itself doesn't even exist in time or space, nor does it have a cause. Time, space, and causality are all purely human frameworks imposed by our cognitive processes: to suppose that space has any real existence simply because you perceive it is, again, a category error, akin to supposing that the world is really yellow-tinged just because you happen to be wearing yellow goggles.)