The eye relief on my scope does not very any appreciable amount, and FHT fixed at 16x really locks it down.
There is a parallax centering technique where you back your eye just out of the full site picture distance, causing a vignette effect, a black ring around site picture. Keeping it centered can assist in reducing parallax/off axis errors.
What is most noticeable is massive reduction in ambient light for the cupped eye. At first the site picture is dim, then as my pupil opens up the scope image becomes very bright, more easily dominating my left eye image with both eyes open. For some this could impact focusing ability.
Jury is out on influencing scores...