The short answer is no, though it’s hard to pinpoint precisely when the World War I and World War II—or First World War and Second World War—monikers arose. During World War I, of course, nobody knew that a second global conflict would follow closely on the heels of the first, so there was no need to distinguish it as the first of its kind.
After initially referring to the “European War,” U.S. newspapers adopted “World War” once America entered the confrontation in 1917. On the other side of the Atlantic, meanwhile, Britons preferred “Great War” until the 1940s—with the notable exception of Winston Churchill, who reminisced about the “World War” in the 1927 volume of his memoir The World Crisis.