Today on preflight i discussed the issue with my highly regarded colleague, answer: what displayed in the CRS cannot have any influency on following the LOC properly. I was PF, so i checked it on our approach 06L at PMI. Man, i can tell you, this plane did strange things.
Final course is 59 and i tried to intercept with 69 in my CRS selector. It went straight offset to the right. Changed CRS to 59 - deviated to the left and intercepted the localizer. Once established i played with the CRS selector: turning right, plane went to the right, turning knob to the left, plane went left of localizer - witchcraft kept my plane offset not trying to follow the localizer as supposed to. My fellow was staggered as he didn't expect it at all, and well i would have been staggered too without being involved in the discussion here.
Learned something new about my highly sophisticated plane. Good thread
Cheers from our crew hotel at Palma.