No, it doesn't have to be upright but it makes it easier and keeps the clutch units from falling out of place. If you are sure the lugs were intact and not cracked and the unit has enough oil in it, then I'd suggest attaching a pressure gauge to the main pressure port on the trans and see if you have any pressure. If not, then it's possible that the convertor wasn't fully seated in the pump gear before the trans was installed. That would mean the pump is likely toast at this point. If you have pressure, then the spline in the convertor that engages the input shaft may have stripped and then you have no drive into the trans.

Just thought of one other thing. Unlike the 727, the 904/999 oil pump is two seperate halves that need to be aligned when reassembling. If they are not aligned, the pump may not fully seat in the case. If the pump is not fully seated, there would be a huge internal oil leak at the pump gasket which would mean no main pressure as well.