It's isn't clear to me how the color information in cr2 and regular files differs and whether there is anything in there that helps with NR.
The primary difference is that RAW data is linear (like when you clicked the Linear box in DPP) and in a rendered image it's usual that a gamma tone curve has been applied. As you saw when you clicked Linear, the data straight from the sensor is dark and sort of squished together. The gamma curve lifts and stretches shadow data and compresses highlight tones. This brightening of the image, like any other brightening operation, increases noise. So yes, it's easier to suppress noise while the data is still linear, for example Dave Coffin's Wavelet NR used in UFRaw. Still, there are plenty of dedicated NR applications that do excellent treatment of rendered images.