Short answer, Yes. For example, my Mark 1 Akubra hanging in the hallway has the side patch of my Unit from another Century which is a rectangle with a diagonal dark green on top and white on the bottom.
These were also the Unit patches previously worn on the shoulder of the uniform.
But the Corps colour on the Vehicle Tac Plate is diagonal Red over Yellow in a square.
Confusing what ?? but even so,, ARMOUR RULES OK