Does reinstalling Mac OS X change the cycle count of battery? If we go to System Information > Power in Apple menu, we see a parameter that is the cycle count of the battery. if we reinstall the operating system, will that remain the same or reset to 0?
The cycle count will remain as it is. This is read from the battery directly.

Like a car odometer, you shouldn't expect to be able to change the cycle count without replacing the battery. Being able to change the cycle count would be dishonest for the next person.