If they do, they are considered combatants. If they don't wear uniforms and have a responsible chain of command, they are illegal combatants.
We should just say the Second Amendment overrides the Geneva Convention, which it does BTW, and allow the civilians to arm themselves at least as well as they could at home, say in Texas.
Rush usually does a good job, but on this he is wrong.
Non combatant doesn't mean unarmed. Police are not soldiers, and are armed. Many citizens are not "legal combatants" but are not unarmed.
Michael Yon has been known to pick up a rifle while acting as a journalist. That doesn't make him a combatant. it makes him armed.
If you are an armed non-combatant, you may not go on offensive missions, but may hold your position, and fire back. You may clear your immediate area, like a homeowner clearing his downstairs.
You may recall that non-military security types were murdered in Fallujah. They were armed.
Having said that, I am sure that military JAG types would recommend to commanders that they disarm people, or have VERY high standards for permitting people to be armed.