Rumours that the AI has unlimited ammo date back from the STW period, but even back then they were not true. You can test it in a bridge battle, where your archers will be hampered. The AI is simply less efficient with its archers, even more so in MTW. And remember that when fighting the Mongol Horde, the AI withdraws HA that ran out of arrows to replace them with new HA, which causes it too appear that their archers actually have unlimited ammo.