That may depend on the environment you use and for how long you treat the sample. Kumar et al., Current Appl. Phys. 14:3 (2014) 491-5 showed dipping GaN samples in ammonium sulphide diluted in aqueous and alcoholic solvent produced increased Schottky barrier heights at room temp. For long, high temp. anneals S may diffuse into the GaN and eventually through the GaN into the Si substrate and cause reactions there.

Good point. Depending on the temperature, sulfur can propagate through the GaN layer, segregate near and on the surface.

It should be tested experimentally, of course, but I can estimate a propagation of S into GaN, especially for GaN/Si sample. In this case the red missmatch (between GaN and Si) is really high, this leads to bad crystalline structure of GaN epi-layer with a lot of disslocations.

Of cource, the thickness of GaN, the time of threatment and the used atmosphere define the final result.