you may have a cracked hose ***Your cooling system generally runs significantly hotter when the Air Conditioning is running. This is due to the extra heat produced by the A/C condenser located just in front of the radiator. You most likely have a defective radiator or cap, or a very small leak in your cooling system. The increased heat from the A/C causes increased pressure in the cooling system, and the leak becomes more evident.
Antifreeze could be running out often due to a leak. It is important to inspect the radiator for small cracks or smoke.
( NO ) with the engine cool
yes you can?
Find where it is running out and repair the cause.
It will overheat, unless you can successfully air cool it.
directly in the radiator while the van is running
Glaciers are akin to giant bulldozers, scouring away soils, plucking and breaking larger rock formations, sometimes with rivers running through them that move massive amounts of material.
antifreeze does two things. It keeps the water in the radiator from freezing in the winter, and helps prevent if from boiling over and evaporating in the summer. You can run your vehicle with water alone in moderate temperatures and it will do the job. But, if you mean by "running out of antifreeze" you mean there is no liquid in the radiator, then yes, your vehicle can overheat and ruin the engine.