No it won't, the US has clearly stated that a fundamentalist regime like Iran will not be allowed to take place in Iraq even if that's what the Iraqi's want.
Now that's democracy.
And sadly it is what a lot of them think they want. History teaches us that when a cruel dictator is gone the people will start to gravitate towards that which the former leader hated the most. (Just look at the nationalist feeling in Yugoslavia post-Tito) Those Shi'ites were savagely repressed by Hussein and now they want to get in with Iran who they see as their real ally, rather than the Brits/Yanks. Some people have no gratitude.
Still not all of the people in Iraq want to be fundamentalists. It's time the Kurds got their own place - they'd be a far better and more reliable ally than the rest of the 'Iraqis'