cpu cooler does not affect the gpu cooler
overclocking can be done on gpu, cpu or in both, but the gpu will not overclock your cpu, at all
you must overclock your cpu
the gpu can be left alone and it can overclokc itself a bit or you can overclock it a bit more by using msi afterburner or similar tools
if you plan on overcloking your cpu on the stock cooler, the temperatures will raise alot, the cooler will not be able to handle it and you will have lots of issues
also the noise, with lots of heat, lots of noise from the cpu fan, so if you plan to overclok your cpu, you need to handle temperature properly and while doing that handling the noise
what cpu do you have?