Endorsing that you read the other thread, WN.
In simple terms, for any A/P - F/D ILS, the receiver gets a 'left' or 'right' signal from the LOC. L or R of what? It has to have some datum. If you mis-set the CI, then its 'datum' is mis-set too. So, suppose you have the CI 45 degrees right of datum and you are closing from the left of the C/Line on the same 45 - the a/c gets a 'you are left of the C/Line' signal. All OK. Now as you approach the LOC so that the intercept geometry is triggered, the a/c will look at the numbers and say 'Cracking! I'm on the LOC'. Next it will get a hard fly left signal which will spoil its and your day. You can think of it in simple terms as being like a VOR intercept, although the 'mechanics' are quite different, but - which heading does the a/c turn to on intercepting? The heading set in the CI window?
I'm not sure what will happen in an LNAV intercept, since I have never been 'authorised' to do one. Why the 737, (Classic and NG) cannot put up a warning if the CI differs from the database QDM for the selected runway I do not know. Other a/c automatically set the ILS QDM on the CI when the runway is selected in the FMC - even easier!