Assuming that camera manufacturers can eventually make the perfect sensor that introduces no electrical noise to the signal, at what point (measured in ISO/area of a pixel) will shot noise be so prevalent that you cease to get useful images?
Here's a good simulation of the 'perfect' sensor that you describe (one having zero electrical noise, thus recordning every incident photon perfectly) reacting to widely differing levels of light, from 0.001, 0.01 & 0.1 photons per pixel (top row), 1, 10 & 100 photons per pixel (middle row) to 1000, 10000 & 100000 photons per pixel across the bottom row.
Click for a larger version where you can make out individual pixels. Image by Mdf some rights reserved.
You can't specificy ISO sensitivity without knowing the saturation point of the sensor (without saturation there is no overexposure), so for your hypothetical 'perfect sensor' you'd have to chose an abitrary saturation point, making the ISO values computed for the images arbitrary too.
However to answer your question it appears about 1 photon per pixel is the limit of getting meaningful images (the top right image, with 1 photon every 10 pixels, looks unrecognisable to me).
It's hard to provide a definitive answer to your question, because it depends on what you subjectively deem “useful”, as well as on many other factors like the strength and quality of the denoising algorithm, the output medium, etc... Thus, this is not really an answer, only some hints to help you find your answer.
First, about the parameters to consider. The area of the pixel is not really important. Although smaller pixels give more pixel-level noise, you can always reduce the noise by downscaling the image (a side benefit of antialiasing). The really important parameter is the total area of the sensor. Also, readout noise is usually only relevant in the darkest areas of the image, most of the time the main noise source is photon shot noise. Thus, quantum efficiency and fill factor are also important.
Next, I recommend you take a look at this page from ClarkVision.com: http://www.clarkvision.com/articles/digital.signal.to.noise/. It is a very well documented discussion about digital noise, together with models and lots of real-life data.