Hi Evelyn,
Great question! If the stone surface is hard and impermeable, I would not expect the resin to change it in any way. That doesn’t mean however, that resin yellowing won’t change how you ‘see’ the stone over time.
If the stone is soft, it may take up some of the resin as a moisture stain. The best way to know if this will happen is if the stone changes color when it gets wet. If the answer is yes, then resin will do the same thing.
If the stone is dyed, then I would expect resin to change it as well. The dye will likely leach out into the resin.