Norman would shout "Peter Parker is Spider-Man" for hours on end.
I don't think he would, actually. He likes to keep Peter's identity as a "trump card" for himself and maybe a few select others if it benefits him (I.E. Mac Gargan during the Millar's run).
But if Norman exposes Peter to the world, then all the leverage he has over him is gone and he's no more of a threat than any of Peter's other villains. That's why he was so pissed when Peter did reveal himself, because he was "breaking the rules".