Unfortunately the GTX 570 will not do NVENC because the chip does not have the video encoding hardware needed.
You might want to consider upgrading just the graphics card to a newer NVIDIA 600+ ("Kepler" or newer) series card and employing its hardware encoding rather than having the CPU to all the work.
There are arguments for and against this. The CPU X.264 encoder just looks better, but CPU load is considerable. The NVENC capable GPUs do take a hit when they have to encode, but that hit is a lot smaller.
I have a highly overclocked 2600K and I have streamed with both options. I always end up using NVENC because I can stream at higher fps with less impact on the game. My observation has been that streaming anything that moves a lot (First person games, but also stuff like Starcraft 2 where the map focus moves constantly) is overall better to do on NVENC. Streaming games that move slowly, I'd use the CPU for better quality.
I find that my games are mostly GPU limited, by a far margin, so I suggest a GPU upgrade rather than CPU/motherboard.