Most noise is not caused by variance in the photon count. On an area as large as a sensor pixel (many times larger an a grain of high speed film) it makes very little difference. Instead it is literal signal noise within the electronics themselves which is then amplified along with the signal as the ISO is increased.
The algorithm you're describing is more or less how current noise reduction technology works, it uses context of the surrounding pixels to guess how much noise affects the current pixel. More advanced ones have edge detection and other features to improve the result. Even the, it's not very good.
When talking about black and white specifically, how you convert the image can greatly affect the amount of noise in the final image.
There are many methods for converting an image from color to black and white. The favorite (and Adobe recommended method) seems to be the "Black & White" adjustment. This method is actually not very good. It works by calculating the desaturated pixel and then multiplying the value based on its hue angle based on the sliders you select. This is essentially signal amplification, which also amplifies noise, so any slider with a positive ratio (a value above 50 in the Black & White adjustment) is also increasing the noise in those areas.
On the other hand, using the channel mixer uses a weighted average of three values. It is much easier with this method to avoid the signal amplification trap because all three channels sliders can be under 100%. The green and red channels usually have less noise than the blue channels, so you can lean on those two when possible to reduce it further. My go-to starting point is
[R 60, G 90, B -40] then adjust from there.