How one perceives a line in space can vary with the perspectives created by different head/eye positions. However, the degree of perception error will vary from person to person and with the amount the head is moved. When some people move their heads, they still might perceive the CTE line accurately (i.e., the perception of the line might not change with head position). For other people, the CTE line or the line of the shot might look totally different with different head positions.
For people who are interested, I have some good illustrations and demonstrations related to this topic, along with some supporting resources, here:
Placing one's "vision center" accurately and consistency is a very important part of both aiming and sighting. One value I see in many "aiming systems" is: the pre-shot routine they encourage might help foster consistent alignment.