As it stands, I'd wager that a great number (if not most) of the Shias see this as their golden opportunity to nail the Sunnis. I don't think they care whether their government is "Iranian-style" or anything else -- this is payback.
Also, besides the exiles, most of them really have no clue what democracy means or why its beneficial. Even the dumbest East Asians I know can look at Japan or Taiwan and kind of "get it." But there is absolutely no example for the Arabs. It is not at all irrational for them to suppose that a theocracy might improve their lot. It's ignorant yes, but not irrational.
Perhaps the tribunals of the criminals, mostly Sunnies, but some Shiites and even some from the Christian communities, may help change their minds about the virtues of a secular law and satisfy their need for payback. A few ropes will insure that payback is a bitch.