Photon shot noise (http://en.wikipedia.org/wiki/Shot_noise#Optics) is as fundamental as diffraction - it's a property of light, not a property of the sensor.

If your sensor counts a mean of 100 photons per pixel, then you'll see shot noise with standard deviation of 10 photons in each of those, for a signal-to-noise ratio of 10. If you quadruple your pixel size and now measure 400 photons per pixel, then your SNR goes up to 20.

This is why bigger sensors (more captured photons for same light level and exposure time) are fundamentally better at image capture.

Ok this is getting pretty convoluted. I didn't mean to imply that photon noise was not a real thing, just that diffraction is a more direct concern. Photon noise can be amortised by a number of different processes which aren't applicable to the case I was trying illustrate. You can't amortise diffraction errors by longer exposure or better photon capture. Pixel size is a primary concern regardless of its noise characteristics.

Think about shooting with a shotgun at a target. If you have a thousand pellets, the distribution of pellets at the target will be quite smooth. Now, shoot through a narrow aperture that takes out 99% of the pellets. Now you have ten pellets. The distribution can not be smooth. The sampling frequency (pixel size) at the target does not matter much. It is the aperture size.

I realize that is a very flawed analogy but it's the quickest I could come up with.

Here's more: http://en.wikipedia.org/wiki/Shot_noise#Optics

To get such less noise you not only need to utilize advanced materials, but also cool down the sensor considerably. To register single photon impacts you'll need to cool down to 0K I guess :-)

Not at all, just look at the difference in the current sensors on the market. There's a wide range of performances due to engineering restrictions. Only the pixel size and aperture size are really relevant to diffraction so it occupies a different class of problems.

Even if you had 100% efficient sensors, photon shot noise would still be an issue. You are sampling the photons emitted by the target. After having reasonably efficient sensors, it's a baseline you can't go under.

I'm not sure about that minimum, but I do know noise (dark current signal non-uniformity for those in the know) increases considerably with temperature. So yes it matters.

FWIW, the rods in your own eye's retina are able to register single photon impacts.