I can't speak for the carriers warehouses, but I do have some experience dealing with carriers/drivers. I deal with shipping/receiving all 3 major carriers (USPS /UPS / FedEx) on a daily basis at my work. When I'm giving them dozens of boxes to deliver, they'll put them on the truck with the label up. I've never asked them why...I'll make a point to ask Monday. When they're delivering, and are having trouble finding a box (they know how many boxes are to be delivered at any location), they'll wander about the truck, looking at all the labels, which are invariably facing up. Based on this, I'm going to assume that whichever side of the box the shipping label was applied to is facing up the vast majority of the time.
Another thing to consider concerning this is that the scanners have read the label.