It’s pretty clear that the major Shiite parties have pretty close links with Iran.
The Badr brigades, which control large parts of the south were trained there. A majority of the influential clerics come from there (including Sistani). And links in general (trade, others) are becoming closer, it appears. I don’t think that Iran is “pulling the strings,” but the relationships are likely to grow. That’s part of the reason why a sovereign and partially democratic Iraq could be a nightmare for Washington, which has been working hard to prevent it.
Could get worse from their point of view. The Shiite population in Saudi Arabia, door, is in the area of SA’s largest oil concentrations, and might be encouraged — probably already has been — to resist the harsh repression to which they have been subjected and take some control of their fate, maybe also linking to the Shia complex that seems to be emerging. And it could get still worse, from Washington’s point of view.
How the US would react depends very much on the popular mood here. That’s the problem we should be facing. Speculation is idle.