The advantages of overclocking are that it allows you to get the maximum amount of performance from your system that you can. You push your hardware to do more work, and therefore get more speed. But, some parts are "made" for overclocking and others aren't. For instance, the "k" models of Intel Chips have unlocked multipliers which allow you to boost the voltage going into the chip, while those that are "non-k" models don't, and are generally supposed to be run at normal speeds.
The stock cooler for most intel chips is made to provide adequate cooling for the chips at stock speeds, hence the stock name. While you can push the i5-3570k using the stock cooler, it is not generally recommended. I would normally recommend a Noctua NH-D14 or Corsair H-100 for anyone looking to overclock.
Edit: You could also grab a Xigmatek Dark Knight or a CM Hyper 212
And no, any OC' Id trust to a stock cooler would be of too little significance to be worth the bother. Not a procedure I'd recommend to someone new to overclocking tho, ....... however wit today;s built in protections, unless you purposely defeat the protection mechanisms, it's pretty hard to break things.
A $30 Hyper 212 wud solve that problem
Step up to a Hyper 612 or Muhgen 3 if ya got $50 to spend
Wanna go to the max, $85 will get ya Phanteks PH-TC14PE which is the current fav.....not as quiet as the Silver Arrow but slightly outperforms the Arrow and DH-14 while giving ya 5 times the warranty.