We tow a 2007, one of the first years AWD was able to be towed 4 down. As several people have commented, having the charge lead to the toad battery eliminates the dead battery issue. The individual that installed your tow package on the vehicle should have hooked that up.
Second, one individual is correct, you have to make sure the key is turned to the off position. For me, I just put in in neutral, then turn the car off. If will not go into the lock position without the transmission being in park. If you have one those fancy push button, refer to your owners manual or dealer.
Third, my Edge is a heavy vehicle, 5,600 lbs! I imaging yours is not much lighter. Do not attempt to tow this vehicle without brakes in the toad. I have a 38' diesel and I could definitely tell the difference until I installed the toad brakes. Also, if you tow in the mountains like I do out here in Colorado, watch your temperature gauge. It will rise, so throttle down, keep you RPMs up at a decent range (2000-2100 for me) and take your time going up hill. Enjoy. Jim G