Some impact - yes. USA's participation by itself means that the American public would be more sensitive to world affairs. What went on in Geneva would be written in newspapers, people would read about it, know better what went on, maybe give more support to 'ending injustice'. Some difference, yes. Much of a difference (as in, stop any war/invasion), no. The LoN simply didn't have instruments to prevent anything, and the USA didn't have the force to be of any difference. It is hard to imagine the USA raising an army just so it can be used to prevent Japan from invading Manchuria, etc.
What would be important though, is that America's participation in the LoN would mean that American administration workers would better know about the flaws of the LoN - you work there, you know what dosn't work. It could significantly affect the UN charter, reforming it in such a way to remedy old flaws. Again, this wouldn't be much of a difference (nation states simply won't want to limit themselves too much), but one nevertheless.