To me, it would matter greatly, because it would be the 'word' of the author. Imagine if a text was found, which was absolutely proved to be the very word of Jesus (if there is such a thing as 100% proof outside the world of weird and slightly scary alcoholic drinks), would Christians reject it saying that they preferred to make up their own interpretations, thanks very much? They would certainly debate it, but they would not necessarily reject it. Likewise, I would not reject a new text by Tolkien, but assimilate it into my view, and it would quite possibly change my view of something if I could see that this text proved that Tolkien intended something else to that which was originally published. Again, if it could be proved that he intended something else and the recent discussions over the new edition of LotR show that this is
not always provable!
Hmmm, this brings to mind the various arguments which have raged over the 'meaning' of the works of Plath. To some, to
many, for years she was writing as a feminist poet who raged against the actions of her errant husband and her whole output was judged against these standards. But with more biographical information it gradually became clear that she loved her husband intensely, and her poetry was carefully controlled and measured. Now, with these new critical opinions based on biographical information, again it became hard to discern whether this information (e.g. the journals, only relatively recently published) was in fact 'correct', or was it carefully released by the Hughes estate to improve their own image after the vituperative criticism first seen?
This example shows how, if indeed something was 'found' on whether Balrogs had wings and Elves had pointy ears it might easily be questioned anyway. We'd ask "Ah, but did Tolkien intend that?", "When, exactly, did he write this and why did he not include it?" and maybe even (possibly, I admit, just in my dreams
) "Is this only being released to stop Barrow-Downers tearing each others' throats out?"