Nah, there are other things you could more accurately pin it on. That moment only really led to Stark involvement, but there would've likely been a succession war soon enough even without what came from that slap.

[hider=Spoilers from the books]There are two other things you could blame for the war that would have made a much larger difference had they not happened this way.

If Jon Arryn had not been poisoned, Ned wouldn't have been brought south thus Robert very likely would have lived a lot longer. No dead king, no honorable Hand to stir shit up, not succession war. Following this theory, you could sorta blame the war on Lysa Arryn and Littlefinger, since they were the ones behind the poisoning.

You could also go back farther and point the finger at Cersei and Jaime. If there was no incest going on and no question of the father of the heir (by way of it really being Robert's and having the dark hair and such), there would have been no grounds whatsoever for a succession war and the idea probably never would have gotten into Stannis or Renly's head, and even if things still happened the same otherwise Ned would have fully supported Robert's son taking the throne so there wouldn't have been any drama in the North.[/hider]