It is highly unlikely that U.S. participation in the League would have prevented or even postponed World War I. The terms of the Treaty of Versailles had been unfairly punitive to Germany, including the famous "war guilt clause" and the imposition of exorbitant reparations. The United States did, in fact, through the Dawes Plan, attempt to help Germany in making those payments; however the bitterness and resentment from the Treaty--which Woodrow Wilson signed on behalf of the United States--remained.
When the League attempted to censure Germany, Italy and Japan for aggressive acts, those three nations resigned from the League. Even had the United States been a party, the League still would have been rendered impotent. At the time, the United States was more concerned with disarmament than defense; so the end result would have been the same.
A more pertinent question might be if a fairer Treaty of Versailles would have prevented World War II. I think the answer to that question is an unqualified yes. Hitler would not have been given a platform, and the territorial demands of Japan might well have been satisfied.
Of course, anything is possible and we can never know for sure what could have happened if history had been different. However, I would argue that US participation in the League of Nations would not have stopped WWII (the most immediate "future global conflict") from happening.
The reason for this is that the US would not likely have been a very aggressive member of the League of Nations. It would not have been likely to push hard for intervention at any of the points that led up to WWII.
For example, a major failure of the League of Nations came when it did nothing to stop Italy's invasion of Ethiopia. Another came when it did little to try to stop Japan from invading Manchuria. The US would have been very unlikely to push hard to prevent either of these invasions. The reason for this is that neither of them seemed to have any significance for the US. Neither was in an area that would have seemed vital to the US. Therefore, it is unlikely that the US would have pushed for aggressive action (war?) by the League to stop them.
The real problem with the League was that its members were not motivated to stop the things that led to WWII. The US would have been no different because the events that caused the conflict would have seemed too distant and therefore irrelevant to the US.