The neat thing about a HUD is that the image in it is effectively overlaid on the horizon. You have a virtual image at an infinite (for all practical purposes, a given distance in reality) distance. This means that as you move your head around, the image will stay fixed relative to the surrounding scenery. This is the feature which enables the flight path vector to actually show where the aircraft is headed, and also enables military HUDs to keep other aircraft boxed regardless of how the pilot positions his head.
If you think about it, banking does not change the viewline straight ahead for either pilot. Even if it would, it wouldn’t be a problem for the reasons given above. The marginal vertical displacement in a bank is not really a factor at all.
Regards,
Fred