According to the Boeing Maintenance Manual, the A/P uses the selected CRS to refine its intercept calculations
- absolutely! If you have ever forgotten, like I have, to reset the ILS QDM after a hold and watched the a/p try to spear off into the bundu looking for a localiser, you will realise that. Leaving aside the appearance of the display, I guess that if one established on the Loc in heading select and then asked it to track the Loc it would, but I have not tried that. I have a suspicion that somewhere in the 'works' is an input bias of 'expected' track and that it might just fly an offset centreline, however.
We used to 'play' with the BAC Lightning ILS on the occasional 'offset' ILS beam and found that you could make the machine track down one edge of the cone and fly the centreline, but that was O L D technology