We know they do, in many novels I've seen real world military history referenced a lot. I don't mean ideas borrowed from, I mean direct references. Like in dialogue and conversation.
In one novel, Victor is conversing with one of his siblings and it somehow turns into a reference to how that sibling has been running a simulation or wargame of an army that got stuck fighting Russia in winter, not sure if it was a Napolean or WW2 reference off the top of my head. He asked if th e simulation/wargame was taking into account just how bad the winter was that year, then pivoted to asking how/why that sister was doing that as her academic major was something else entirely, and she replied something like "I have electives" to indicate she was studying some military history as an elective. I think it was Yvonne.
That's just one example, I can remember about 4 others from sourcebooks as well as novels.
Also, think about how the references in Battletech that are just loaded with real world history. From Northwind Highlanders and their ties to Scotland, to the FWL invoking King Arthur with the Knights of the Inner Sphere. They aren't afraid to pull directly from even Arthur legend. Do I even need to mention the Marians? They weren't exactly Roman scholars, they were periphery bandits who set that up. But they knew plenty about the ancient Romans. A guy named Ethan Allen established the Green Mountain Boys. Mercenary units with names that are historical references, that's a whole lotta historical or mythological knowledge plugged into the Battletech universe right there.
If there is one thing Battletech is consistent on, it is digging up LOTS of real world history and particularly military history. In light of that, one can only conclude that cadets at military academies are very familiar with these topics. It's the only sensible explanation for just how often these references make an appearance in-universe. I mean BT really beats the military history references to death sometimes.
They probably are biased to shared history of similar cultural influences. For example Great Houses where the primary culture is that of European heritage, studying fellow Europeans from history. But that doesn't exclude or preclude other stuff from popping up. Since lots of sub-cultures exist within each Great House.
Beyond that, feel free to use your own imagination to plug in who is taught what. In practical curriculum terms, it could literally change based on what's popular and vogue at that moment, or even stem from which professor they got for whatever class. If you are in Mr. Harding's 3:30 seminar, he's fond of Sun Tzu. If you got Professor Keating at 5 p.m., oh boy you better know who Wellington was, and if you don't, you are about to.