Na, the box would have to be badly and noticeably damaged for something like a playstation to be DOA, QC should at least power up every unit before it ships, these are not cheap $20 toys...
Boxes are more sturdy than you expect. You can shift a box enough to disrupt an already bad solder job without causing visible damage. Especially if every box literally has zero room to move and an entire freight shipping unit (container, tightly wrapped pallet, etc) was moved/tossed around roughly due to a mishap or whatever.
And many electronics failures don't even need the shipping variable. Something can turn on a few times just fine, and then not turn on again. Those previous tests could have caused a temperature rise or fan vibration to ruin an already bad connection/solder somewhere.
There are so many variables, it's unreal. It'll happen to the Xbox One. It happened to both the PS2 and PS3. Probably happened with the first PlayStation. I personally had a DOA PS2 - discovered it was DOA on Christmas morning. That was a joyful moment, btw.
It happens less frequently after launch because everything is much less hurried. The production floor has become more "expert" at assembly, inspectors can better see what fault tolerances there are and when something they see is likely to cause a unit to become DOA after some shuffling or repeated testing.
It happens with every piece of consumer electronics. Why does this cause a new discussion every single time? Highly hyped launches get more attention, and more DOAs I suspect, due to the amount of product that needed to be manufactured, assembled, and moved. But everything from handheld consoles, normal consoles, smart phones, tablets, laptops, TVs, hell probably even the more gadget-y kitchen appliances... depending on a few variables, like product sales volume and whatnot, and degree of complexity/number of internal wire and solder connections, the likelihood of DOAs rises.