Yes, but you have to script it. Your script would have to detect the appropriate dead unit (easy if this is for an Intro or something, more tricky in the middle of a firefight), get the civvy to walk over there and perform an animation, remove the weapon and magazines from the body and add them to the civvy.
If I remember rightly civvies can use pistols and rifles but they can't use rocket launchers and machine guns becuase they don't have a secondary weapon slot.
Kill list ... I suppose you could do it with event handlers.