Its come to my attention that until modern times, the big prollem with armies was that they traveled on their bellies; it wasn't until late-industrial period that some military genious glommed onto the idear that caravans of supplies was thought to be a good idea.
I have in my library an interesting book entitled,
Alexander the Great and the Logistics of the Macedonian Army, published in 1968, and available online at Abebooks.com. It discusses how Alexander supplied his army with food via advance procurement in the areas he was marching into, supplies carried by his troops on their persons, by their servants, and baggage columns, and additional supply columns from where food was available for purchase or impoundment to where his troops were operating. Persian interception of a Greek supply column of 500 wagons was one of the reasons that the Greeks were forced into fighting the Battle of Plataea in 479 B.C. under less than ideal terms for them. Supply columns have been around for a much longer time than the late-industrial period. They were an especially critical item in any form of extensive siege operation, as the besieging army would rapidly eat the immediate area clean, and be dependent on regular supply columns from then on. Large numbers of horses were a special problem due to the need for grass forage for them.
It seems that military units should be able to pillage their way to health / survival - and not rely on home country for anything - and can't become more than 3% of population until industrialization (max 10% then) and become extremely cost-prohibitive thereafter.
I would suggest you read an account of Napoleon's advance and retreat from Moscow in 1812 with respect to that idea of pillaging their way to health and survival. As for units after the introduction of gunpowder, military units were highly dependent on some supplies from the home country in the form of gunpowder, replacement weapons, and replacement personnel. Your idea is only valid if the military unit is moving through a good agricultural area immediately following the harvest, as occurred with Sherman's March through Georgia in November and December of 1864.
Perhaps some sort of 'caravan' type thingy, that if intercepted generates massive amounts of commerce, otherwise the units depending on it for supply are starving and would run amok into the region to satiate their wants, desires and needs...
Such a unit already exists in some of the scenarios of the game, particularly the Age of Discovery, but you cannot make units in the game dependent on supplies. Factoring the need for supply into any game is extremely difficult, and rarely succeeds. I have in my game collection a game published by Simulation Publications Incorporated called "War on Ice" about a hypothetical war in the Antarctic, where the entire game is based on supplies. It is completely unplayable.
That is a very documented issue concerning medieval era vassal forces, i.e., I raised them in accordance to my vow of fealty to you - My Lord - but they're now 1500 miles away and they have nothing to eat, My Lord, what shall they do?
Such problems occurred during the Crusades, where the response was getting access to a port where supplies could be delivered from overseas, supply columns or local merchants then moved the food supplies to the needy units, and typically the men would then be given money to purchase their own food. Of course, there was nothing to keep merchants from heavily charging for the food.
Note, the food requirements for men and animals have not changed to any great degree over the past Five Thousand or so years. Somewhere between 3 and 5 pounds per man per day, along with at least one gallon of water, with horses requiring about 9 pounds of grain and 10 to 12 pounds of hay per day, along with a minimum of 5 gallons of water, and oxen requiring about 20 pounds of hay or 50 pounds of grass, along with time to process it. Then time processing food for oxen, as in "chewing the cud", is one reason why oxen move slower then horses. There is quite a lot of information on animal rations in Sir Garnet Wolseley's
Soldier's Pocket Book for 1886. I have a copy and it makes for interesting reading.