Yes, you should buy an aftermarket cooler up front.
At full load, you won't see 60c with the stock cooler, and it will be noisy.
An inexpensive $30 one like the cm hyper212 or xigmatek will do well for any reasonable oc.
In the mean time, It will be easier to install, run quieter and cool better than the stock intel cooler.
I really hate to tear down a working production pc after I built it. Many things can go wrong. Better to do it up front.