Seems like it would be a real but minimal effect.
A little trigonometry says that for a 737-8, with the main gear about 20 meters behind the nose, and a crab angle of 5°, the nose would be offset about 1.7 meters upwind of the runway centerline when the main gear are centered either side of the runway centerline.
For a 3000-meter runway, with a TD zone 500 meters down the runway (2500-meter LOC range), the nose being 1.7 meters left or right of centerline would show a 0.04° needle deflection downwind at the touchdown zone.
And since full-scale deflection of the LOC needle for an ILS is 2.5°, that would mean the LOC needle deflection would be about 1.6% of the full deflection.
Probably less than the width of the needle itself!
Longer runway or shorter airframe (731/2/3/4/7) or smaller crab angle - the LOC needle deflection will be even less. Over the threshold it will also be even less. Longer airframe or shorter runway or larger crab angle would result in more visible deflection.
Someone can check my math - sines and cosines were never my favorite subject.