I can only speak for Marine infantry, but no; Monghol tactics are not part of the training. Expeditionary Warfare focuses on Assymetrical models, what euphemistically used to be called "guerilla" although manuever warfare is much much more refined than say a Nicaraguan revolution. You just need to render the enemy useless, which does not require annihilation.
Prior to each combat deployment we still have a capstone training at 29 palms where we conduct a combined arms exercise on an objective. I like to run through the squad/platoon level ops with my guys, but for the BN level exercise, I like to be up with the forward observers for air/arty and sniper. Once were in country, there's really no place to watch an operation of that size and see the whole thing at once, but I've bermed and cleared 5 cities in Iraq - we don't burn, loot, rape, pillage and kill. We search, seize, detain bad guys, and leave everyone else to carry on with their lives. We want to remove the cancer, not kill the body.