AFAICT (not being an expert by any stretch of the imagination), Saddam became nothing more than a figurehead once Baghdad was occupied. As has been suggested before, capturing Saddam is a political victory. It nominally turns the Iraq war into a success, even though it's not clear that capturing Saddam will materially affect actual conditions on the ground. Even if his foot soldiers draw their inspiration from him being their commander, it's up to them to believe that he is still directing them. If these guys hang out mostly with each other rather than the general Iraqi population, it's entirely plausible that there'll be an "echo chamber" effect in which they all convince each other that Saddam's capture is merely American propaganda, they got a double and are lying about the DNA tests, etc. IMHO, we need to be wary of a similar effect here at home, with the message being that Saddam's capture is tantamount to victory. We don't really win until we can leave without the country falling apart.
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