It's entirely depends on if the UN keeps up sanctions and more importantly if the US and U.K. continue the No Fly Zone and at times No Drive Zones.
If they do when another Shia uprising occurs his troops will bog down meaning central Iraq a genocide zone. Likely parts of Northern Iraq as well as the Peshmerga try for land. We are talking millions dead and the country destroyed and Iran and the Sunni jihadists would end up with what was left.
Wouldn't that level of mass slaughter have caused the U.S. to intervene, though?
Now if the US and UK ends the inspections and NFZ and sanctions then Saddam even demented would have the uprisings put down again with hundreds of thousands ending up in mass graves again. The regime from Chemical Ali on down even on autopilot knew how to put down rebels as long as they weren't being helped by Western air power.
Would the Iraqi Shiites have even rebelled again if large-scale Iranian and/or U.S. support was not forthcoming, though?
Also, what happens to the Iraqi Kurds in this scenario?
However in the longer term if Uday or his brother would have been capable of filling his shoes in a religiously radicalized cauldron which Iraq was slowly becoming I don't know. In protecting the regime with the faith movement he created something that put religious extremism above himself and his family that was going to bite them on the ass hard eventually.
So, you're thinking of an Islamist takeover of all of Iraq?
Also, if so, wouldn't that trigger Iranian and/or U.S. military intervention in Iraq?