Downsampling in and of itself, does not address noise.
Reasonable downsampling includes a lowpass filter. A lowpass filter reduce the energy of any signal/noise within the stopband. SNR tends to be poor at high spatial frequencies.
I don't think noise has simply a pixel level effect where averaging neighboring pixel luminance values takes care of the problem (won't Bayer interpolation do the same?)-
High-quality Bayer reconstruction usually tries to keep sharp edges (guess image information that is unknown), meaning that it tends to be vulnerable to sensor noise (even amplify it) unless great care is taken.
-noisy images still look noisy at different magnifications other than 100%. So noise is like waves on a ocean, at different scales, you are still able to perceive noise in the frame just like you can still see the surface of the water is not flat.
Why do you think this would work and what have you been trying?
I like extreme examples. I am not saying that this is what happens, but I hope that this will make you think through your claims.
Imagine that a line of pixels should have had luminance values of:
[17 17 17 17 17 17 17 17]
(signal has no high-frequency components, only DC)
Then imagine that the pixels have been read out with an error ("noise") turning it into:
[16 18 16 18 16 18 16 18]
(noise has only a single frequency component, and seems to be deterministic)
What do you think averaging would do?
In the real world, signal and noise are not perfectly separated in the frequency domain, and it is extremely hard to change one without affecting the other. It seems that practically usable algorithms exist, though, where some (small) loss of signal quality is accepted for a significant reduction in perceived noise.