Except that literally every single economy in the last 150+ years that's ever been jumpstarted has been done so by war, thus proving the fallacy - though seemingly illogical - completely incorrect in practice.
Much like socialism.
The only thing that makes your statement true is if you read from Keynesian Economists who approve of government spending. If viewed by, lets say, a realist or a capitalist or free market economist, war spending does nothing but put the nation into never repayable debt.
For example: did it ever cross the minds of the Keynesian economists that the reason the US was lifted out of the great depression, 2-3 years
after the end of WWII, was a result that most of the industrial world in Europe and Asia was blown to shit and the factories in the US tripled in size, to supply the world with its needs? Russia and Germany were decimated after the war, two extremely large manufacturing powerhouses but the consumption of world was still there.
You can find study after study, opinion after opinion on the results of WWII and the economy. Some saying that its directly responsible for getting the US out of the depression, some say it was FDR's New Deal (even though that was passed many years before) others saying it did nothing of the sort. I fall in the later category. *edit* - its a classic case of the welfare warfare state in action: one group of idiots (Welfare Statists or, more commonly known as Socialists) think that government spending through the socialist and Fascist policies of FDR's New Deal was responsible for lifting the US out of the depression and the other group of idiots (Warfare Statist) think that spending on WAR RAR!! lifted the US out of the depression.
The same can be said of college loans: were more or less loans issued prior to the US federal government guaranteeing the repayment of student loans? Since the guarantee, has the
higher learning industry exploded to meet the new demands? If the federal government guaranteed repayment for all the nations broken windows, would there be an increase in the manufacturing and installations of broken windows after the guarantee? In order to pay for all those broken windows, its going to inflate the window industry and remove money previously allocated into other aspects of the economy. Its the same thing for the war economy.