Well in the short term given no eruption, no massive ash cloud, no 'year of winter', no crop failures, no massive die offs of livestock, and no national crisis the US seemed to be heading toward an intervention in the Great War of the side of the Allies.
In his memoirs Wilson was always extremely vague about about the possibility. He never unequivacly stated one way or the other if it was a real possibility. Of course once the eruption took place there was no chance of teh US getting involved. America needed all its resources to deal with the millions of refugees evacuating out of Wyoming, Colorado, Utah and other states hit hardest by the ash fall. The crop failures led to severe and unexpected food shortages. There was a wave of religious hysteria as preachers from one end of the country to the others declared it a sign that the end times had come.
It took the US economy a quarter century to fully recover.
While there was not a massive ash fall in Europe they were also effected by the year of winter as both sides suffered, though the Russians, Germans and Austrians suffered worst. With the US economy in ruins there was suddenly no more capitol available for loans for the Allies.
In June Russia collapsed into civil war. By September Austria was falling apart and French soldiers were openly mutinying, and there were food riots throughout Germany and the occupied territories. Millions of civilians in Poland, the Balkans, the Baltic, Rumania, Russia, Belgium, and occupied France would starve to death as there was simply not enough food. Britain was in the strongest position and even they were bankrupt and facing massive strikes at home and a growing revolt in Ireland.
With both sides falling apart and unable to even feed themselves the result was the October Armistice. It halted the fighting while leaving the armies in place. It was not meant to be a permanent stop to the war but turned into one as neither side was capable of restarting the war.
Germany and the British Empire could be called the 'winners' as they expanded the most. Germany occupying Belgium, Luxemburg, norther France, much of Poland, and incorporating about half of the former Austro- Hungarian Empire. The rest splitting up into Hungary, Czechoslovakia, and Yugoslavia. France lost all the territory the Germans were occupying at the time of the armistice. Italy suffered over half a million casualties and was unable to claim any additional territory. The Ottoman Empire was torn apart with much of its territory being claimed by Britain either directly or through puppet states. The Russian Empire disintegrated into sixteen independent ethnic states, many of whom are backward and warlike dictatorships.
The world since has been one of constant struggle as temperatures have dropped and the evidence indicated the world has begun a new Ice Age. Scientific advancement has been severely retarded as resources have needed to focus on food production with the remainder going into military armament. Since the end of the Great War there have been countless small border conflicts all over the globe as nations and empires fight for resources and food producing lands.
Without eh Yellowstone Eruption the world today would certainly be a brighter and warmer place.