Yea, CM 212 has some issues with some cases due to it's size. Stock coolers are fine for 670. But if you wan't a better cooler then CM TX3 evo is the way to go for you. It fit's in most of the cases and is cheaper and is really close to cm 212. You can even add an extra fan to it if you wan't more cooling.
The stock cooler will do the job, particularly if not overclocked.
The only downside is that the stock 92mm fan will spin up under load and become noisy.
Even with overclocking, the cpu can tolerate heat. It will downclock to protect itself from damage if necessary.
If noise becomes bothersome, look for a downdraft type cooler with a slow turning 120mm fan.
As to the possible benefits of overclocking the cpu,
run these two tests:
a) Run your games, but lower your resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited, and overclocking would help.
b) Limit your cpu, either by reducing the OC, or, in windows power management, limit the maximum cpu% to something like 50%.
This will simulate what a lack of cpu power will do.
Go to control panel/power options/change plan settings/change advanced power settings/processor power management/maximum processor state/
set to 50% and see how you do.