Propaganda Failure

You've probably heard from time to time that leaving Iraq would be a massive propaganda victory for Al-Qaeda. There's also the fear that Iran will gain more power. That would only make sense without an understanding of religion in the Middle East. First Iraq is run by a group of Shia politicians. Iran also happens to be run by a Shia government. This mean, as happened recently, that Iran would actually help Iraq's safety by backing their government. Al-Qaeda is a Sunni group and therefore the Shia Iraqi Government would have no interest or desire to allow Al-Qaeda is exist within Iraq. They are viewed as infidels and heathens. That's like people saying that if Martin Luther had taken over the Vatican it would have been a huge propaganda victory for extremist-Catholics.