An assassin wouldn't be facing him in open combat. The Thu'um wouldn't be useful if he didn't know he needed it. That being said, his knowledge of the Thu'um would probably prevent people from trying to take the throne the way he did.
I don't think Ulfric is an easy Jarl to assassinate in the first place, just look at his room in the place of the kings. You have to go through a lot of small and linear corridors each connecting to guard rooms that are well lit and guarded by some of the most fierce and devout soldiers in all Skyrim and I believe there would be even more of them after Ulfric becomes king.