One thing that interests me though is that traditional water profiles are such because that what was available. Could you potentially make a stout BETTER by (for example) softening the water or using the water that's local to you? Does hard water by necessity make stout work better or just make emulation easier?
That's a difficult question to answer, since it comes down to your own determination of what's best for you...for example, you might prefer to drink dark ales, stouts and porters that don't have a minerally flavour profile.
Many beers become famous because they are brewed the same way over decades or indeed, centuries, using the local water. As matho suggests, some compounds will change the mash pH which in turn will make subtle changes to the end product. For example, I use very soft water here in Canberra and I used to struggle getting a decent conversion with my stouts, porters, schwartzbiers etc. Then I fiddled with the mash pH by adding some Calcium Carbonate or Bicarb of Soda to push up the mash pH and I found I obtained significantly better conversion. That said, I never ever added any chemicals to my mashtun when I made pale ales and lagers thanks to the soft water - unless I wanted to try to emulate the waters of Dortmund etc etc. So, it was more a matter of knowing what I was making the beer with and adjusting the water profile - if I need to or could be bothered!
Although I had better conversions with my dark beers by chemically changing the mash pH, I'm not inferring that I necessarily made a better beer.
Getting back to your original question, I think it would be a pretty harsh judge who would criticise your stout on the basis of the water profile - assuming you aren't using foul water to begin with! With enough practice, it is possible to identify hops used in a beer (memories of an excellent evening at Ross's house many moons ago readily come to mind!) and in some cases, the yeast strain, but water chemistry is possibly a bridge too far!!
In my particular instance, I do find my stouts are better when I treat my water, but that's only because my water is so soft and the darker grists seem to do better in the mashtun when I add a teaspoon or so of the right compound. That may not necessarily apply to fellow brewers in Adelaide, or Perth or Melbourne etc etc...And lets face it, you can have the best water profile in the universe and easily stuff up a batch with crap yeast, or stale hops etc etc, so it gets back to my original mantra - fresh ingredients, temperature control and patience! Sounds like a new album title from the Foo Fighters!!
Cheers,
TL