I don't know the answer, but I am going to speculate a bit.
As has been mentioned, assuming you keep the aperture and shutter the same you aren't actually increasing the amount of light entering the camera. What you are doing is boosting the signal (with it the noise) so that it moves the data into the brighter half of the histogram--towards the right. I think this would be advantageous because you would be moving the data into the region of the histogram where the sampling rate is higher. The signal to noise ratio would be the same, but the gradations of light sensitivity would be finer.
I think that you will not see a difference in noise-performance because boosting in camera (increasing ISO) or boosting in post processing (exposure slider in ACR) achieve very similar results. With that said, I have come full circle because one of the main purposes of ETTR is to increase the signal to noise ratio. Your strategy doesn't accomplish an increase in SNR. It only allows you to capture more tonality within the dynamic range that is present.
There is no magic here. If you are working at 1600 ISO and are underexposing by 3 stops, you are not much worse or better off than going to 12,800 ISO and having the "correct" exposure (aside from the fact that you will recover some shadow detail at 12,800 and it will be total crap). The details of these relationships are not precisely the same for all manufacturers, but generally speaking these relationships hold true.
So you get half-credit for your approach within the limitations you describe.