Could it be done? Yes, easily. The US had a ton of good will post 9/11 that was fully eliminated by invading Iraq. Going after a known host country of the terrorists who committed it would track and ending the genocideS there against the people in Darfur and S Sudan would be salable to the international community. The US had good relations at the time with Egypt, Chad, and Ethiopia (particularly Egypt). Eritrea, which has their own issues with brutality, would probably oppose it, but they have no close political allies to speak of then or now. Iraq had a large, somewhat modern, military. Sudan would be completely defeated in days.
Fallout:
Iraq would be more developed, and if his not-crazy son was the one to take over there would probably be some small amount of a thaw in diplomatic relations. Iraqis in general would be no worse off than the Kuwaitis or Qatari. Probably still have the US protecting Kurdish interests in the north, though.
No Iraq invasion probably leaves Syria in a stronger position without having to worry about elements across the border causing issues for them. ISIL doesn't come to power and there's no wholesale destruction of world history in the area or looting of museums in the area.
Darfur is a huge area. An independence referendum in the area would create a very large new state being on the edge of the Sahara.
As you can see, Chad would be the most instrumental in getting to this area quickly.
S. Sudan may be slightly larger in order to encompass all of the oilfields in that area. American oil exploration would probably amp up with the country starting as an occupied zone. Pipelines going through Kenya may be a good track to take as it's a more stable country with good relations with lots of western states. The chances of the current interethnic conflict in S. Sudan are probably lessened as they become independent in stages as a monitored process (like that used in Iraq).
Most of the remaining population of Sudan is centered on the Nile and is more homogeneous than one would think (compared to the extremely heterogeneous S. Sudan). It would now almost certainly become a hotbed for fundamentalism with the Sauds spreading their evil unchecked from just across the Red Sea to a young, humiliated, and poor population. There may be no ISIS-Like group in Iraq, but there would be a very good chance of one developing in Sudan, imo. Particularly so if there was any kind of postwar power vacuum at all.