Will Iraq become a super-charged Qatar?

Marc Lynch (Abu Aardvark), here

"...What kind of role Iraq might eventually play in Arab politics if its domestic politics continue along its current path (i.e. Shia-dominated, sort of democratic, no collapse into major violence) and if efforts such as Amr Moussa's push to integrate Iraq into the Arab order succeed?
I suggested that one plausible scenario is that it might become a kind of super-charged Qatar: an American ally which has good relations with Iran, a lot of oil money, some endemic problems with Saudi Arabia, and acts as a kind of swing vote in inter-Arab politics. Is that plausible? Would it be in America's strategic interests? And how would the original Qatar feel about it?"