I'm not too sure about that. About the difference in taste? Yes, it's going to be negligible. But I do think that different mineral concentrations in varying waters will impact such factors as yeast development, rise time and thus gluten development. While I was a member of a breadmaking forum, one member from NM went through a tortuous process of trying to figure out why his dough did not rise. Eventually, the problem was identified as lack of minerals in his RO drinking water supply. Possibly an isolated, extreme case, but it still makes me think that some development interaction with yeast can be attributed to the chemical makeup of the water.
I really don't think a blind taste test could pick up this difference. The difference would have to be in the crust's spring, chewiness and (to a small degree) flavor. I don't think some TV-show kitchen would be as rigid on the parameters as anyone here.
It does seem to be an experiment worth trying, if anyone (points @ Pete-zza) is interested in volunteering their effort.