There is nothing in COE rules about loaded or not.
Yes it does, it clearly states in 327.13 which deals with COE property.
§ 327.13
Explosives, firearms, other weapons and fireworks.
(a) The possession of loaded firearms, ammunition, loaded projectile firing devices, bows and arrows, crossbows, or other weapons is prohibited unless:
(1) In the possession of a Federal, state or local law enforcement officer;
(2) Being used for hunting or fishing as permitted under § 327.8, with devices being unloaded when transported to, from or between hunting and fishing sites;
(3) Being used at authorized shooting ranges; or
(4) Written permission has been received from the District Commander.
But with the possession of ammo in the same sentence it might make no difference.
http://www.handgunlaw.us/documents/COERulesPamphlet.pdf
I have read plenty where some interpret that carrying unloaded is permissible ( based I think on the transportation clause in (2) ), after reading the above link, I don't think I would without written permission.