I'm not sure I understand why people are calling a lock on this thread. Bernie seems to think F1 is a lost case in the USA. My guess is he also thinks the same about Europe, because his concern is not public support, is ... money.
I think this quote, attributed to him, says it all (especially the part I bolded):
taken from ESPNf1.com
"We've got maximum two races in America, and when you consider the country is as big as Europe and we've got several races in Europe, it's difficult," he told Al Jazeera. "If we had a lot more races there and a lot more television, it would be okay. We've been there, years ago, and it's a little bit like the rest of America, they want to see a profit before they start something and it's not easy to do that."
Apparently, and if we take out the money issue, what Bernie says is that F1 can never be successful in the USA because it can't have more than 2 races there. And I say this is a total nonsense. F1 covers the WORLD and although americans from the USA are very "domestic" in what they like, there's no doubt there's a following for many major international events too.
Now, would it be better if american drivers from the USA were racing in F1? Would it have the impact Schumacher had in Germany or Alonso in Spain? I guess so, but I do doubt that this impact is as huge as it is portrayed to be. A new "surge" of fans would show up, but they'll be short lived. And F1 will always live as it has always: like the most elitist, pinnacle-of-racing, form of motorsports. With enough following to be successful worldwide (including in the USA).
So, replying to the OP, I'll say: no, an american driver wouldn't do much for the following of F1 in the USA. Sustained TV coverage and one (or two) Grand Prix being held in the USA will.
And I'll end with one example:
Dan Wheldon. I bet very few people in the UK knew that a british driver had won the Indy 500. Another:
Dario Franchitti. If I ask about him to a bunch of people somewhere in England I bet many will look at me and say they don't know italian drivers that much.
Why? Because in the UK you don't get easy access to Indy coverage. And you get no race in Britain (I know it's not supposed, Indy is a domestic series from another country anyway). So, you can have excellent drivers from the UK winning everything across the pond, but that doesn't create a following in their own country.