The GTX970 doesn't need a cooler, no. Although you might see a small benefit at this stage, I'd advise you not to mess around removing GPU coolers if this is your first DIY build.
Some people do remove the stock cooler/backplate and fit an AIO or custom waterblock though. That's usually if they're OCing it and/or running SLI. If you OC the GPU it can get pretty toasty. Likewise, SLI setups get hot due to lack of airflow between the cards.
I'd like to try OC'ing as this is the first time i'd have a build capable of such. Hence why im buying components like the 6600k.
Do you think i can OC the GPU much with the stock cooler that it comes with?