I'll side with the pessimists (wow, what a surprise, I know).
Interwar US had neither the actual military power, nor the international outlook & will to provide the LON enough 'oomph' to make a difference.
Also, as noted above, institutions like the LoN or UN are fine and dandy if wars are the result of misunderstandings or confusion. They're not so helpful when wars are the deliberate result of conscious calculation (however incorrect those calculations may latter turn out to be) and/or intention.
Consider the classic bar-room moments: It's easy to keep your buddy from accidentally getting into a fight - watch where he goes, keep him from stumbling, etc. But stopping him from slugging someone whom he's consciously decided to take a swing at is a lot harder.