Up until when I left, that is the late 80s/early 90s, I never saw anything published that encouraged getting any type of formal education whatsoever, which is what you would need to learn an ancient language. There was no form of education in Biblical languages beyond the "tibdits" served in articles and the like via the Watcthower Society or if you went to Pioneer/Elder/Missionary School. Not even Franz had enough knowledge to teach it beyond this.
Because of my family's background and my father having served in the U.S. Airforce, my family and siblings learned several languages while I was growing up--so it is possible to learn a living language this way, I can tell you. But Biblical Hebrew and Aramaic--you have to know both to read the Old Testament-- and you have to really get some help there. And knowing koine Greek is not enough to understand the Christian Scriptures because you have to also know the type of Aramaic of the first century Jews--it was a mishmash with some Hebrew terms mixed in--because there are several sections in the Greek with Aramaic transliterations, not to mention others which depend heavily on understanding the play-on-words of the Jewish culture that the gospels come from to comprehend what was being written in Greek. Nothing like this, as far as I know, has ever been offered or recommended by the Witnesses.
While they've never outright discouraged it, each place they warn against higher learning is a big X against learning ancient languages formally. You just can't mail away for a course or get it in high school. It won't be enough to run with the big dogs. Some scholars spend their entire lives, from youth onward, devoted to learning just one facet of an ancient Biblical language. Try and catch up with that!
I doubt there is anywhere in any writings of the Watchtower Bible and Tract Society that tell Witnesses that they cannot learn the original languages per se ("new light" for me since I've been gone for a very long time). But how will you explain that you've had to enroll as a member of a Baptist or Catholic university and join something like the Catholic American Biblical Association or the United Bible Society so you could gain access to certain texts for hands-on study to the elder body of your local congregation? Believe me, the Jewish Antiquities caretakers aren't just going to release materials on the Dead Sea Scroll to just any Tom, Dick, or Harry that says: "Hi, I'm learning Hebrew. May I please have a look at the Q scroll of Isaiah?" So I don't think truly learning the languages will go over with celebration by the Governing Body once they learn of it.
A footnote to having the original writings: The theological stand of Christianity--Catholic, Orthodox, and Protestant included--is that the revelation from God as contained in Holy Writ includes--not excludes--the editing process.
For example, if not for the editing process, Genesis as both the Jews and Christians have now would be missing the first chapter and half of the Noachin Flood account, not to mention much more that was added onto this book through the ages.
The teaching is that the books as finally accepted by their religious communities--in their canonical form--represent inspired revelation as God intended. So the argument that not having the original originals is moot because often, as understood by Judaism and Christians, writers and orators of the narrative sources did not know that they were playing a part in the revelation process that would eventually be considered as God's Word.
That may not be acceptable to those who don't accept the Bible or God, but that is how they've accepted it for centuries. You can look it up in references such as the Judaic Encyclopedia and the Catholic Catechism of the Catholic Church or books like the Zondervan's Bible Handbook and similar books. To Jews and Christians, it is the final product that is the Word of God revealed.
It is the same for a writer--it is the final draft of a book that represents his true intentions, not his first or second one, or a movie director that makes a final cut or special edition of his film and says: This is the movie I wanted audiences to see the first time around, and this is the one I want them to remember as the definitive version.