I'm not talking about understanding WW1 as in what we all learned in high school history class, but rather, the actual politics of the time. The specifics of the Treaty of Versailles. The atmosphere during the early 30s and the power moves done then.
Can you understand the war without it? Probably not. I'd say you roughly need a good understanding of European politics in the interwar period, especially the chip on Germany's shoulder over Versailles, to really get to the root of Hitler's Nazism movement.
That said, it is not necessarily the case that WWII should be seen simply as a byproduct of WWI and Versailles or a continuation of the first war - the story is more complicated than drawing a straight line of causation would suggest. It's obviously important - un-excludable, even - but it's not the only factor that played into Nazism and the coming of WWII.