Given that the term 'Warrior Monks" could cover military/religious units as diverse as the Knights Templar, Kali Cult Thugs, Shaolin fighters, or the Hashashim 'Assassins', much, much more could certainly have been done with them. At the very least, a method (Civics Card, Religious Pantheon, Apostle/Guru interaction?) to allow specialization or differentiation of your 'Monks' into one of the very different groups mentioned above would be appropriate.
They can never be Game Winners, because they are bound to be superseded in the Modern Era and later - although, in an Economic Victory DLC/Expansion, perhaps Warrior Monks could morph into a Corporate Assassin/Sabotage group of hirelings in the Atomic/Information Era. . .
After all, the game has never been completely historical, and the GDR is proof enough that the late game is essentially Fantasy, so why not a Shaolin Warrior Monk training facility that starts teaching Hacking of Corporate Data Bases or international financial thuggery? Or is International Financial/Corporate Thuggery already being well-taught at the Harvard Business School?