Well in that case, then it will all depend on the design of the engine and/or the oil filter. OP did have a point about how the oil pump doesn't behave like a cup pouring cold oil like in the videos on Youtube. That freezing honey oil might be flowing better than we think when it gets past the pump. It definitely won't be flowing good enough to protect an engine if it's hot, but it's lubricating a cold engine nonetheless.
Sorry not sure I follow what you meant at the end there regarding not protecting an engine if it's hot....?