Your post is a bit confusing.
I don't think so. My post makes a very reasonable assumption that you are in the real world, and can't come close to saturating the sensor in many situations, without getting motion blur, or shallower DOF than desired. That is where choosing aperture and shutter speed come in.
By gain I gather you are referring to amplifier gain, which is increased in high ISO settings. CCD system gain is reported in terms of electrons per ADU (alalog to digital unit) and is the inverse of amplifier gain.
While a CCD gain of 1 electron / ADU would be perferable, this would require 16 bit encoding with most current 35mm style cameras, which can record 50,000 electrons easily. The full well of the Canon EOS 1D is ~79,000 electrons and a gain of 1 e/ADU would require 17 bits (inconvient).
Again, this is the real world. The current DSLRs can barely deliver 9 or 10 bits worth of really useful information. A nice, clean 16- or 17-bit readout is a pipedream at this point in time for most people. Maybe some of the expensive MF backs do better, but base ISO perfomance on most cameras is abysmal.
Also, I think that if in some miracle, a way of reading/digitizing sensors that only includes poisson and dark current noise were made available, that there would be any reason to stop at approximately 1 ADU = 1 electron. Another bit or two would keep the posterization noise down. I wish we had that problem. A clean, 16 or 18-bit digitization of the sensor charges would eliminate the need to change ISOs; ISO 100 under-exposed by 4 stops would be as good or better than ISO 1600 is now, even with the same well capacity.
While total noise in absolute terms increases with increasing exposure up to full well (according to Poisson sampling), the signal to noise ratio is best at full well. See the discussion by Roger Clark.
I've done this research myself. I have a spreadsheet with the noise values at various RAW levels at various ISOs from my 20D; I used this data to determine if other people with 20Ds and 30Ds, especially, really had noise problems in their cameras. In every case it turned out that the noise levels were the same in these cameras, and that it was either exposure or conversion that was emphasizing noise.
For optimum S/N one should expose so that the sensor is full well in the highlights and this is related to lux/seconds and not the ISO chosen. If you expose for full well and use an ISO higher than base, clipping will occur with 12 bit AD converters unless the camera has a setting to vary CCD gain, which is usually available only on specialized cameras for scientific purposes.
Again, you are assuming that shutter speed and aperture are not real issues. They are really the most important thing to choose in many situations. Full exposure at ISO 100 is not an option. For a lot of wildlife or spontaneous night-shooting in city streets, a full histogram at ISO 1600 isn't even possible.
I think that ISO 50 on some Canons sets the gain to 1/2x, and there is a risk of blowing highlights with this setting.
ISO 50 is probably implemented as an arithmetic trick in most cases, which loses a stop of highlights, relative to the metering. In some, ISO 100 doesn't use full-well (Canon 1dmkII), and 50 actually uses a little more of the sensor's DR.
If you expose at less than full well, then the amplifier gain can be increased. Absolute noise will be reduced, but so will S/N, and this is not what most of us want.
No, that's not what we usually want, but that is often unavoidable.
Anyway, you seemed to miss my point - Once you have decided what aperture and shutter speed you want to use (low sensor signal is the primary cause of noise), the *highest* ISO will give the least noise, especially in the shadows (clipping being the only danger).
Let's say you take a shot at ISO 400, and you review the histogram, and notice that there is a stop of unused highlights in the histogram. You can fill that histogram in two ways; by decreasing the f-stop and/or increasing the exposure time, or by doubling the ISO (some cameras have intermediate f-stops, but they are not always real). The former will decrease noise, but you might be sacrificing sharpness or DOF, or the lens' sweet spot. Increasing the ISO will also reduce the noise, not quite as much as increasing the sensor exposure (but more than you might think), but there is no compromise on the Tv and Av settings you want to use.
You seem to be replying to me as if I had written "You get the lowest noise by using the full RAW DR, regardless of ISO", which I did not write. My original statement was one with a condition - that you have aready chosen the f-stop and shutter speed you want. There is no option for full-well exposure in many cases of the condition.