Nope, parallel with the bottom of the oil pan. Orientation to the pump body is un-important. What matters is that the pickup is flat to the bottom of the pan. Otherwise, one 'end' or the other of the pickup will be higher than the other, relative to the pan bottom, and that's an opportunity for it to 'suck air' under hard acceleration or hard cornering, and you really don't want that.
Having it pressed in and fully seated is indeed the way the factory did it. However, the factory also used a special tool to do that job such that it applied constant, even pressure all the way around the pump pickup tube so as to ensure that it was not deformed even in the slightest and thus had a very tight fit in the housing. Most of us don't have such a tool and have to resort to using a hammer and some sort of tool alternating on the 'sides' of the pickup to walk it in to the pump. Doing this almost assuredly will deform the tube a little bit, perhaps enough to make it loose enough so that it will eventually work its way out of the pump - with disasterous results if it happens while you're winding out second gear at wide open throttle. It might happen, it might not --- it's one of those "do ya feel lucky?" propositions. Another positive solution is to weld a metal tab the the pickup tube such that it can have a hole drilled in it and secured under the nearest oil pump backing plate bolts. The pickups that Milodon sells for use with their replacement 'kickout' pan come that way.