Effectively, it depends on how violent the eruption is...
However, the climatic effects of the eruption will influence the events of World War II, in that depending on what time of the year Yellowstone erupts, will effect the harvesting season of 1941...
Almost certainly, there will be mass famine globally, for the next couple of years, due to the ejecta entering the upper atmosphere.
(The 1942 growing/harvesting season will be abysmal to say the least, if possibly non existent in the Northern Hemisphere, due to the above...).
You can make the argument that if Yellowstone erupts in 1941, than World War II effectively ends on that date...