Of course any Illuminati that you have in mind as relating to Ancient Greece will have precious little to do with the historical freethinkers of Bavaria. So in answering this question, I am safely untethered from historical fact, and find myself adrift in a world of which Meek Mill raps “I don’t have to join the illuminati just to get a new Bugatti”. 
Yet even in this fondest flight of Conspiracy Theory, I have to pause and point out that to the ancient Greeks, Egypt was the site of magical and poorly understood lore, and Greeks only occasionally understood what hieroglyphics were about.
If Greek could be used to translate all those other ancient languages, they had a funny way of showing it. Like the Chinese, and for the same reasons, the Greeks were relatively incurious about other cultures — up until Hellenistic times, when people from those other cultures were themselves writing in Greek.
In any case, the only things Greek does that Latin doesn’t are a greater propensity towards compounds, definite articles, and the optative. You could argue that makes Greek better suited for translating Sanskrit, and perhaps German. It would be a pretty tenuous argument.
Though it would be an argument that the historical Bavarian Illuminati would no doubt approve.