Just wondering if the transponder mode C reported altitude will be off if the pilot accidentally has the wrong altimeter setting.
No your altimeter setting has no effect.
The altitude signal for mode C comes from a separate pressure altitude sensing "blind" encoder that only supplies the transponder, or an equivalent device integrated into the transponder itself, or a pressure altitude signal coming from an Air Data Computer on a larger aircraft. It reports pressure altitude to a resolution of 100 ft. So as you are climbing between 1000 and 1100 ft, ATC's indication will roll over from 1000 to 1100 at somewhere around 1050ft, from 1100 to 1200 somewhere around 1150 ft, etc.
So if you make the wrong altimeter setting and level at a cleared altitude and the pressure altitude reported by your transponder is off by more than 1 or 200 feet from the pressure altitude they expect to see, ATC will inquire about your altimeter setting.