If you mean a chest in battle - yes, the AI does it when it has no better action. Works the same way as with crucifixes, coffins, dwarven statues, statues, etc. If the AI unit has 1 more AP and they have a chest or structure nearby, they will usually remove it from play - unless the AI feels that it's overpowering you, in which case they rush for your lines rather than destroy or pillage.
If you mean a pile of gold on the map... never seen it happen.
As for the runic staff, I would venture to say that the developers meant they can strike from distance.
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