When the Stormcloaks were ambushed prior to the start of the game,what would become of the rebellion if an overzealous soldier killed Ulfric then?

I think Galmar would take over.

Galmar would have taken up the cause though maybe not so political as Ulfric Stormcloak. Would the Civil War continue? I believe it would have though its footing would have been lost.

I'm pretty sure that without Ulfric, the rebellion would be crushed pretty quick. Maybe it would be back on, if a new leader rose, but I don't think any such person exists in the SKyrim as we know it.

The civil war would go on, and Galmar would take over. If you go to the Stormcloak camps and listen to people, you will never hear anyone saying "I am fighting for Ulfric." They all say they are fighting for their religious freedom, or because their family members were kidnapped and killed by the Thalmor. None of that changes if Ulfric is dead.

Granted, I do not think it would go as well for the Stormcloaks without Ulfric. But everyone would not just give up because he was not there anymore.

Now we would have a more tranquil land of Skyrim.

exactly. Ulfric was the steam in that rebellion engine. but someone else would rise up again. I don't think they could do it as well. galmar is to brash and maybe even a little wreckless. No one has the charm and charisma that Ulfric has.

If anything his death would set fire to more Nords to join the cause which was why Tullius meant to do it so quickly in Helgen instead of say... the capital Solitude.