Nah, you can solve that by just using more expensive tech (ie higher adc bit depth and faster sampling). The cool thing is that it's doable!
It depends on what the noise sources are. If you're ADC limited, sure, but if you're limited by something else--detector noise, air turbulence affecting the signal, variation in LED output, noise in the room--a better LED won't help.
Except it will a long way down. The random noise would have to match the characteristics of human speech for there to not be information that's possible to gather in an uncoded system.
That's an interesting claim. It's true in theory--the information is still there--but what's actually going to do the separation of the noise from the signal?
One would have to characterise the system and apply pretty rad filtering.
Actually hmm, I don't know if machine learning or neural networks or genetic programming have been tried on this, but it sure does sound like something they could work at!