"Are you sure this is true? I see the Sunnis as a very organized armed force, with the training and personnel necessary to take over Iraq again in any civil war. The Shiites seem disorganized."
The Kurds are well armed and can field a considerable army. The Shia have their own militias, which have been being restrained by Sistani.
But in any contest, the Sunnis are only 20% of the population. They have the Ba'athist organization, and a few tribes, but they'd be facing all the rest of the country.
(Read: CSA versus USA, without any rules or nice-guy stuff, and you get the picture)
In case of a civil war the Kurds would break away and it would be the Shia vs the Sunnis. The Sunnis with support of nearby countries would do quite well, but not well enough to fight off the Iranian Army and the Shia.
It likely could degenerate into a bloody stalemate in the middle of Iraq.