That’s definitely not the case in Europe. Socialist movements were on the verge of power in many countries before WWII, and actually ruled or heavily conditioned the political life all over the continent until the end of the Cold War. The war effort had been dealt with by the early ‘50s at the latest; the following 40 years were dominated by the fight for social and economic equality.
The war “helped” only in the sense that it often acted as a selection for the political classes in the following 20 years or so, in some cases literally (Italy and France).
Socialism gained only after World War I disrupted incumbent powers and wealth. World Wars I and II really need to be considered as a unit. War continued into the '20s in Eastern Europe and then resumes in 1936 in Spain. See "War of the World" by Niall Ferguson.
Socialism was not that strong before WW I destroyed the power structures of the German, Russian, Austro-Hungarian, and Ottoman Empires. The resumption of war in World War II destroyed the Japanese and Chinese Empires and enervated the British and French sufficiently that the British and French Empires dissolved after the war.
The war “helped” only in the sense that it often acted as a selection for the political classes in the following 20 years or so, in some cases literally (Italy and France).