Interesting... I always thought AWD could not be towed 4Down but guess I forgot about Cadillac and how the name used to mean "Quality, Well Built"
Go here
http://www.remcoindustries.com/Towing/Store.php and enter the year make, model and "Drive" (2wd, 4wd, AWD, choose awd from the dropdown)
It says you can tow it with the LP-1 Lube pump kit (1500-2000 installed includes your tow lights by the way).
SO if you can tow it with the LP-1.. odds are good you can tow it engine idling, HOWEVER. i'd be scared of what all that idling does to the engine, epically in a high grit/dirt environment which is where it lives when it is being towed. (I sometimes have to dump a bucket of water on my windshield to rinse the grit off before I unhook that is how dirty the "Towed" position is)