I almost guarantee that Ahmed Hassan al-Bakr would lead the way if there was to be a fight from the Ba'athists, Saddam was a Stalin type of figure, he built up power from behind the scenes and eventually set himself up to be the heir apparent to an aging and increasingly less energetic al-Bakr, who was sort of the Hindenberg character in all of this.
I think the civil war idea is both plausible and interesting. And it still invites the possibility of large-scale American involvement, the more the communists establish themselves as a challenger faction, the more likely the Ba'athists go to Syria and the US for help. OTL the two Ba'athist regimes, despite ideological kinship and the fact that Iraq's party was based off of Syria's did not get along well.
With this civil war the two may draw closer together than OTL, and the US may, consequently, draw closer with Syria as a sort of third bloc against communism, how this pans out with US alliances with Persia and Israel as well is another query.