I was wondering if there's any examples of armies carrying a depiction of the Virgin into battle or as a prominent symbol, crosses and shouting the names of saints seem common, but I have the impression that crucifixes with the actual figure of Christ or the Virgin aren't that usual.
Yes, the Eastern Roman/Byzantine Empire was well-known for doing this. They used other Christian symbols as well, like the cross and the Chi-Rho monogram, but they were very devoted to icons and relics of Mary. In particular they had an icon of Mary (the “Theotokos”, the “God-bearer”) that they carried in battle and displayed on the walls of Constantinople whenever the city was under siege.
There were churches dedicated to Mary, the most important of which was the church near the royal palace in the Blachernae neighbourhood in the northwest part of the city. The city had plenty of relics of Mary too, brought from Jerusalem after the empire was Christianized in the 4th and 5th centuries. They claimed to have relics of Mary’s cloak, girdle, veil, etc…even pieces of Mary’s hair, and maybe even drops of her breast milk. Mary was considered the special protector of the city, and all victories in battle and successful defences against sieges wear attributed to her miraculous assistance.
Examples of this include the Persian/Avar siege of Constantinople in 626. The icon of Mary was carried around the walls, and both sides supposedly saw Mary appearing in the sky, offering help to the Byzantines. The city was saved again by Mary’s miraculous intervention during the Kievan Rus’ siege in 860, both by carrying the icon around the walls and by dipping the relic of her cloak into the Bosporus - suddenly a storm arose and destroyed all the Kievan ships.
If the icon of Mary was lost or damaged in some way, it was considered to be a bad omen for the city. In 1204, when the Fourth Crusade attacked Constantinople, Alexios V carried the icon with him, but he dropped it during a battle and the crusaders captured it. Soon after they conquered the city.
In 1453 during the final Ottoman siege, the Byzantine carried the icon around the walls again, but it was accidentally dropped. They saw this as a sign that Mary had abandoned them and the city would soon fall…and it did, a few days later.
Sources:
John Haldon, Warfare, State, and Society in the Byzantine World, 565-1204 (Routledge, 1999)
Jonathan Harris, Constantinople: Capital of Byzantium (Continuum, 2007)