You will need a motherboard that supports overclocking. Z77 or P68 in this case. That case comes stock with a locked H61 motherboard.
Pushed to the limits you can see about 150W draw from the CPU alone. Your GPU on a good day might be able to pull 60W, so your total power draw won't require much.
You aren't going to see much in the way of gains with such a weak GPU though. Gaming performance starts at the GPU. Unless you are running a game that exclusively relys on CPU for performance you likely will not notice the difference.
Since we are talking a stock HP tower, I doubt you will want to give overclocking a try anyway. You would need to replace the power supply, GPU, motherboard, and case, ideally, to make overclocking worthwhile.