For World War II, it didn't. As Mussolini said, "the League is very well when sparrows shout, but no good at all when eagles fall out". The League of Nations settled some disputes between smaller nations through mediation and sanctions, but had no teeth against great powers, especially with the rise of fascism.
If the title is a typo and you meant World War I as I'm assuming, it would have run into the same problem.
No, sorry, the title is what it means. If there was no resistance to Wilson's foreign policy and the US joined the League of Nations, and supported them militarily, would that have mitigated the factors that led to Adolf Hitler's rise?
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