General, stain resistance is not really related to grain size Directly. But there is a correlation to be made. Steel in its annealed state is colled from the critical (non-magnetic) temperature very slowly. This allows the growth of carbide crystals (grain). Grain size will be largest in annealed steel compared to fully hardened and tempered (softened) steel.
Chromium is a strong carbide (grain) former. A little bit can be a great thing. For example 52100 is a relatively simple iron carbon steel alloy, but is has a very small amount of chromium in it. Not enough to make it anywhere close to stainless, but enough to improve the formation of martensitic crystal structure at very small scales. Chromium can be a good thing for other reasons than just providing stainlessness.
On the other hand, in stainless steels with very high concentrations of chromium, the grain size will tend to be much larger than in simple carbon/iron alloys (the so called high carbon or what I prefer to call low chromium steels).
Lots of chromium makes a steel resist oxidation, but it can also adversely effect the working properties of the steel. That is why some of us are carbon steel knuts, thinking that the overall working properties of low chromium steels are preferable to most 'stainless' steels.
So yes, grain size is effected by chromium concentration, but it is the chromium, not the grain size, that confers stain resistance. Q new technology like Crucibles particle metallurgy techniques are changing all the old rules by radically changing the way steels are made. But that is another story