Don Wheeler
By orifice, I think you mean the hole in the side of the needle that the paint flows through on the 350. I doubt whether it makes any difference. If it did, Badger would have probably keyed it. But, why don't you do some experiments and let us know what you find? The Paasche H is a similar design and it isn't keyed either.
Don
As Don suggests, if you are referring to the machined port on the side of the needle, I can't see that it would make any difference what the orientation of the needle is. Siphoning action will simply pull the paint through the needle, then it's sprayed in the airstream.
Once assembled and the needle is tightend, the threads will determine the orientation of the needles position. Shimming the needle base I guess could change the rotational position, but then it would change the needle tip position relative to the aircap and the airstream.
Patrick