I pillage all the time with certain civilizations.
Zulu Pillaging Division: Archer, Axeman, Impi, Impi.
Mongolian Pillage Squad: Longbow, Crossbow/Mace/Axe, Pikeman, Keshik, Keshik.
It only moves one square, but then the Keshiks or Impis pillage whatever square they move into... even mines on...