History suggests that there's always somebody. In fact, there are always at least two people ready to fight in any power vacuum.
If nothing else, if they're convinced that the war is lost, they'll be fighting over who gets to overthrow the Saddam regime and surrender to the coalition, the hope being that the Americans would let that person serve as a puppet leader in a post-war Iraq.
But none of this seems to be happening, so it suggests that Saddam may still be alive. On the other hand, I suppose it's possible that Saddam is dead and that the Iraqi government is just in complete disarray.