Yes, but then the usage was far less political, except for the broadcasts from Russia and Germany. After WW II, nearly all the services were in some way polarized with "The West" or the rest or sympathetic to one side. Heck, even little Portugal's broadcasts were famous for their pro-Western and "anti commie" stances.However the origins of international shortwave broadcasting go back much further, to the late 1920s and early 1930s.
But one of the major uses of SW even in the 30's was to cover the "home nation" with ones like the classic Radio Prado in Riobamba, Ecuador, being the first national radio voice for that country way, way back in the 30's... even before HCJB began saving indigenous souls.Soft power projection and connecting with the colonies drove the earliest broadcasts. As storm clouds gathered over much of the world with the expansion of fascism in the 1930s more countries jumped into the game, each with its own political message. The advent of World War II brought in the U.S. and a few more countries.
But with a very different focus in most places. SW stations intended to serve all or much of a single nation began to die by the 60's, just two decades after WW II was over.The shortwave broadcast structure was solidly in place by the time the Cold War became a thing.