Yes, you won't have any problem at all. It's a high quality PSU from CWT. The power supply requeriment for your system is: 550 Watt power supply (Minimum recommended power supply with +12 Volt current rating of 38 Amps.) and two available 6-pin PCI-E power connectors. You are able to do SLI with two 470 if you want.
The 470 gtx doesn't require a separate heatsink. EVGA is an impressive brand. All its products have a very high quality.
The GTX 4xx will run hot... so any extra air flow in the case is a bonus. Don't let that worry you though, they are designed to run hotter than prior generations. I only bring up the extra heat they generate in suggestion to your "extra fan" question. The GTX will generally provide your system with more heat that's all....
The Psu is a Good choice for sure. If you ever want to use SLi however you will be looking at a decent quality 850- 1000 watt PSU for longevity sake. (which Corsair is great quality, as Henry said. CWT make great PSU's)