It would be hard to prove it authentic but not inspired since (a) we have no independent test for inspiration besides Tradition (which is absent here)...
Alas, Jimmy has forgotten Fundamentalism, the dowsing rod of God. All we'd need is a blood-bought, regenerate, Spirit-and-fire-baptized Christian to get his paws on the text, wait for the Inner Tingling of Infallible Conviction Free From the Aid of Papist Traditions (TM), and then either Name It and Claim It for all true believers or Cast It Out. ;)
It’s funny, but, in all seriousness, it's pretty much how Fundamentalists (and numerous mainstream Protestants) "verify" inspiration, right? I've never understood how Calvin can defend the internal testimony of the Holy Spirit for an individual Christian without at least countenancing God can and does do the same thing for the whole Church (and confirm that decree with an individualized internal testimony). If the Holy Spirit can work truth claims from a co-worker through my brain and then confirm or deny them in my spirit, surely He can work truth claims through the Pope and ordinary Magisterium without forfeiting the same corroborative apparatus inside me. Calvin’s main hurdle is not how a Christian can infallibly and assuredly hear or sense God speaking in the Bible, but how he gets the Bible in the first place. Tradition trumps the internal testimony from the get-go precisely because we must rely on Tradition to locate an acceptable version of the Bible. Put another way, we rely on Tradition to approach an otherwise random array of ancient manuscripts *as* the Word of God. It’s one thing to say Christian can have the assurance of God *when* they listen to God’s Word. It’s quite another to say any person can “divine” the right table of contents *about which* to feel assured.
A scenario I'm more intrigued by is if we found copies of the canonical works that significantly *alter* their contents. It would not then be a question of changing the canon (the formal bounds of Scripture), but of changing parts of its content (its material bounds). I mean, we already “update” and “improve” biblical editions in light of new papyri, so there is in principle nothing wrong with changing the Bible based on the best scholarship. What is the line between a principled, intra-canonical, textual revision and an outright, extra-canonical addition? I realize, with a sigh, this is about as simple a question as the old metaphysical riddle of when adding grains of sand to a small mound of dirt makes it become a big mound. What's the line between near and far? What's the line between bright and dark? What's the line between a manuscript correction and a canonical switcheroo? I'll have all the answers for you tomorrow, first thing, don't worry. (Riiiiight.)
A crucial point is that Scripture is not exhaustively coterminous with the Word of God. This is the whole basis for revering and following Tradition and Scripture TOGETHER AS the Word of God. God's Word is larger than Scripture, but Scripture is God's Word FOR THE CHURCH. Even a totally authentic apostolic writing would not need to be added to Scripture, since 1) the canon is closed [yes, I know that's a big question still on trial here, but indulge me] and 2) it could still function as God's Word by becoming a living ALBEIT EXTRA-/NON-CANONICAL element of the Tradition. Just as the Fathers, Doctors and Popes of the Church became (and comprise) a living, formative element of the Faith, even without being canonical Scripture, so too would this apostolic "late comer" become formative, canonized or not.
Having said all that, since I think my quandary about significant textual/material revisions to the canon does leave a window open for effectively altering the canon, I think it's important to consider how Trent decreed the canon. Did Trent negatively (descriptively) set the canon, as against Reformed rejections of certain books? Or did Trent positively (prescriptively) define the canon, as against any possible additions whatsoever? In the former case, which I think better accords with the language in the pertinent decrees, Trent defended the fact that the OT, Deuterocanonicals and NT all really ARE inspired and that efforts to remove or suppress them are anathema. In the latter case, which accords with our instinct of “finality” on this point, Trent set ironclad boundaries around what is Scripture, and THEREFORE established that nothing else could ever be Scripture too.
I'm inclined to believe the former (although Trent's defense of the Vulgate is harder to square with certain advances in biblical studies and promulgations in the last half-millennium). I see the same kind of negative dogmatism at work in the decrees on Transubstantiation. As the Pontificator has pointed out very well on many occasions, Transubstantiation does not exhaust the doctrine of Real Presence – it defines it! Trent, in effect, declared there can be no orthodox “theory” or theology of the Eucharist without *at least* affirming what Transubstantiation affirms, to wit, that Christ is really and truly present in the bread and wine, and that his propitiatory offering is not substantially mingled with any thing else (incl. bread and wine). As far as the metaphysical and semantic modes/means of expressing and understanding that truth, well, that’s not really a matter of dogma (i.e., changes in accidents/essence metaphysics may open new vistas of faith without denying the older meaning of the dogma). Point? I see the same kind of negative "line in the sand" dogmatism with the canon. There can be no orthodox canon of Scripture WITHOUT the Catholic canon, but advances in archaeological and textual studies can and may expand upon that dogmatic basis without incurring anathemata.
 Indeed, much of KJV-Onlyism rests on the claim that the KJV’s Textus Receptus, unlike other corrupted (Masoretic, Septuagintal) Bibles, has such an astounding percentage of manuscript integrity (~95%).