I think in the arnett analysis the OP angle is measured against the TVL. So in that case head position does affect the OP readout.
With Arnett analysis, they want 2 ABSOLUTES and everything else RELATIVE to those 2 absolutes.
First absolute is the PLUMB LINE of GRAVITY which is an absolute vertical.
Second absolute is an absolute HORIZONT which is PERPENDICULAR to the vertical. An example of a horizont that is PERPENDICULAR to the plumb line of gravity is the FLOOR.
Head position: Not necessarily how you hold your head normally. But rather how you hold it when you are looking into the distance at a mirror where you see your own eyes; your eye level, your 'own horizon'. There is also should be a ceph stat or a vertical chain that shows the plumb line of gravity, true direction of gravity, absolute vertical for reference.
The Arnett 'TVL' is a matter of aesthetic preference. It's based on what would be considered 'attractive' rather than just the 'norm'. It is a vertical that they want to pass through near the end of your nose BONE and also through the nasio-labial junction where the base of your nose meets the labial ledge area.
Your Frankfurt horizontal might not be perpendicular to this TVL. If not, that's OK. Nobody SEES your FH anyway. What people look at is alignment RELATIVE to the line of gravity (absolute vertical) and the FLOOR (assume it means a flat plane perpendicular to absolute vertical.)
If you give them (Gunson) a ceph that you took ELSEWHERE, they will rotate it so the 'TVL' passes through the points they want it to pass through and they will use a horizont that is perpendicular to that. It might be a horizont parallel to the floor or your FH if it happens to be parallel to the floor.
In essence, Arnett analysis makes things RELATIVE to an absolute vertical and absolute horizont. The rest is where they want the rest of your face to go relative to their TVL.
I put up some links that borders on this topic on the educational section.