Generally a z in the motherboard name will state it's able to overclock (Although I could be totally making this up).
Giving us your motherboard model will let us determine a definite yes or no.
And no CPU cooler and Mobo are some really important factors, but so is the PSU both wattage and the quality, as well as a case with good airflow if you go air cooling. And let's not forget time to perfect a good overclock.