Will repeatedly looting villages bankrupt the AI players' economy?

Even if M&B simulates the economy where amount of goods produced by villages determines amount of goods that are sent to the cities (which I doubt) raiding may not influence economy as much as you think. Because rhodok parties also loot villages, thus supplying local market with the spoils. Also just one party that goes around burning villages'n'rapin' cattle can't possibly damage the economy enough to be devastating to the point where the country is going to be picked apart by its enemies.

While I do believe that the AI does randomly obtain their soldiers (In a slightly reasonable manner), I thouroughly believe that raiding villages/caravans does affect the economy.

Villages are required to make produce and send them to cities to turn into other goods, or sell there. The villages increase their prosperity by selling goods, and the cities do aswell by selling the goods in the city. Some of these goods are exported through caravans to make more money. More goods to sell means more money. No goods coming from villages means less or no money.

So ultimately, raiding villages and caravans does affect AI and human players.