No. It will still track down the centreline of the ILS LOC beam.
The only difference you will notice is the magenta "dagger" will be 182 giving the impression of a different angle of drift.
That's what I always thought as well. However I tried the following in the (A380, so still Airbus) SIM recently. ILS RWY 23, with a LOC QDM of 232, hard-tuned 210 in the NAVAID page, the magenta dagger showed 210 as expected and released the SIM at 6 miles. The aircraft started to turn towards 210 degrees, and subsequently the autopilot disconnected.
It left me slightly baffled as to why it would do that, since I was under the impression the aircraft would simply track the localizer beam, which it didn't. Took a video of what happened but can't share that here. I was always under the impression the course had to be checked at 350ft to make sure the course is within 5 degrees for the de-crab, but somehow more seems to be happening.
Funnily enough, we don't get the AUTOLAND warning light if the LOC signal disappears below 15ft RA, however if you do an auto land in a 30 knot crosswind, how does the aircraft then make sure it stays on the centerline, considering the fact that it could easily drift off in those last 15ft?
Regards,
PGA