I think this is an interesting question, but I am going to be highly skeptical of any attempt to answer it in a concrete way.
I think there are different levels of classical education--at the high end, you've got the full Greek/Latin language scholars who are reading ancient texts in the originals, and that's great, but that's never going to be the object for everyone. Classical education is subject to criticism for being "elite"--and at this level, it has to be. I tend to think of this as "classical scholarship," and it's not happening in K-12.
I suppose you might also consider a deliberate in-depth study of the 7 liberal arts to be the definition of classical education, but again, you're not going to finish that in a K-12 program. "Introduction to the 7 liberal arts" is probably as far as it goes.
But then, there's the whole mythos/logos/dialectic/paideia (ala Norms and Nobility) that would have us reading for meaning and taking instruction for the sake of our characters--in an effort to be a more virtuous person. This is what I think can happen during the K-12 years, and I would not call it "receiving a classical education;" I would call it "being educated in the classical tradition." I think I don't like any terms that make it seem like it's a finished business, but rather part of an on-going process. (In Plato's Republic, his full educational plan takes 50 years!)
I really like the stuff about paideia in N&N. To me, that's an intellectual awakening--an awareness of the intellectual life, an interest in at least some aspect of it, and the ability to read and learn for oneself, accompanied by the desire to do that. Once you get a person to that point, they can, indeed, do anything. Charlotte Mason thought it could pretty well be achieved by age 13 or 14. It's not a "complete" classical education, but it gets you to a place where you could continue it *on your own* if you wanted to. I'm not sure you can do that by 13 or 14 in our current climate, but surely you can by 17 or 18, at the end of K-12.
I'm just enough of a pragmatist to prefer that we focus on what I think is possible, and that is "educating in the classical tradition." If we graduate our students and they never pick up a book again, we probably haven't accomplished it.