I'll bet we do or the next best thing
Remember back in 1995 when a couple of Saddam's sons-in-law defected to a neighboring country, taking Saddam's daughters with them? Odds are we got some DNA samples from the daughters during routine "medical examinations", and that can be enough to identify their father.
Given all of the intel operatives we have working in Iraq, there's also the possibility that someone got a sample of Saddam's own DNA, such as from a hair brush on one of his palaces.
