No. Soldiers were paid with tax dollars, raised at hellacious wartime rates. The result was that business was heavily impacted in order to pony up the low pay the soldiers received. In the meantime, the wartime labor shortage also triggered the mass movement of women into the work-force, which actually worsened unemployment problems when the soldiers were discharged after the war.
Fighting WWII was necessary, but it wasn't an economic boon to the nation.
If you look at unemployment rates from 1940 to the Present, you will see that your assertion is incorrect. In 1940 the unemployment rate was 14.6% for persons 14 years and older and went down to 1.2% in 1944. The umemployment rate from 1946-48 remained fairly constant at 3.9%. It ballooned to 5.9% in 1949 and then started another major decline down to around 3% during the Korean War. The bottom line is that unemployment rates stayed considerably lower during and after WWII than during the Depression Era of the 1930s.
The Great Depression began in 1929 when the entire world suffered an enormous drop in output and an unprecedented rise in unemployment. World economic output continued to decline until 1932 when it clinked bottom at 50% of its 1929 level. Unemployment soared, in the United States it peaked at 24.9% in 1933. It remained above 20% for two more years, reluctantly declining to 14.3% by 1937. It then leapt back to 19% before its long-term decline. Since most households had only one income earner the equivalent modern unemployment rates would likely be much higher. Real economic output (real GDP) fell by 29% from 1929 to 1933 and the US stock market lost 89.5% of its value.
A significant amount of jobs were created post WWII in the US to supply those countries whose manufacuturing infrastructure was destroyed by the war. The US industrial base was untouched and intact fresh from being the Arsenal of Democracy during the war.
The movement of women into the workforce was a good thing for our economy.