What parts are oiled "after that"? Bearings, cylinder walls, pushrods/cups, rockers, cam gears/chains, these are all pressure fed. The pipe analogy doesn't really work, because the pipe you are describing isn't fully enveloped, where the gallery system is, with small offshoot paths where the fluid ultimately ends. If you dump 1L of fluid in your pipe, there's 1L of fluid, regardless of whether it's water, syrup or honey, they will pool or spread-out differently, because you aren't filling the pipe, but the volume is the same.
As long as the oil can get back to the sump (the only real part of the process dictated by gravity) quick enough to prevent the pick-up from being exposed, and the oil is able to be drawn in the pick-up, it doesn't really matter.
But my point was more in addressing this:
Which is simply wrong, as long as the pump is not on the relief. The same volume of oil is being moved through the engine; the flow rate is the same.