Normally (running uninverted) there is some extra space in the bottom of the trans housings for a larger pool of gear oil. When inverted, that changes, since clearance up top was minimal to begin with, so now it doesn't hold much oil. What happens now is that the gears of the input shaft will be largely submerged, perhaps entirely. If you run the "same" oil level as before, or higher, you will probably submerge the pinion shaft & gears as well. So there could just be some friction losses for the gearteeth slogging through thick oil.
What determines the "same" oil level is an interesting question. "Normally" the correct level is 5mm below the oil filler opening. When inverted, that specification is meaningless. Uninverted that equates to roughly 3 liters.
Note that despite what appeared earlier in an otherwise excellent reply, the filler plug does not become the drain plug. The filler (on the side) is still the filler, but the drain is now the breather, and the old breather is now the drain. Terminology I suppose, since you could in theory remove the breather when uninverted to fill it, it's just that you can't get at it in a 911, nor is there any reason to when the 'real' filler is on the side, and more importantly, the correct level was being determined by taking a reading there during filling. A lot of shops fill them to the point of overflow, which is incorrect, and can cause annoyances.