The a/c is programmed:-
a) to setup an 'intecept' on the localiser based on the QDM you have set. If you want a bit of fun, try a VOR/LOC localiser intercept in F/D or A/P with the CRS set 90 degrees off. Don't ask how I know
b) To use localiser deviation as its 'master signal', but a bias of the set QDM is applied as a 'datum', hence the symptom you described. It will initially turn onto the QDM but correct as the deviation signal strengthens, but I believe that it will not then track the LOC exactly. I'm not sure I could work out whether the bars would be centred or not! My guess would be yes.
We occasionally used to 'experiment' in the BAC Lightning on a 2 deg offset ILS by offsetting the QDM by 2 deg and miraculously we flew down the runway centerline.....remaining brain cell cannot recall the ILS display.