From what I've read on these forums from 2xxxk owners is that a nice OC can be performed with the stock cooler. Only way to know of sure is to find some benchmarks for coolers that includes the one you one you own that compares the stock cooler/HS. You could always try the testing yourself and documenting your temps. Copper pipes doesn't necessarily mean it's going to better than one without.
Eventually someone will have the same or a very similar question of yours and may see your findings helpful of temp comparisons.