By definition, stimulus either means fiscal stimulus, referring to additional consumption/spending induced by direct government spending or lowering taxes, or monetary stimulus, referring to lowering interest rates or increasing the money supply through central bank lending policies. Stimulus does not have anything meaning with respect to "benefitting the average American." Defense spending in colloquial usage regarding lucrative contracts or federally managed programs thus is fiscal stimulus.
If the question is more on if defense spending increases the welfare of the median American, whether that be measured through GDP/capita, real hourly wage, or some other metric, it is hard to isolate all the effects of various defense spending policies throughout WWII to today. A good question is to ask about the opportunity cost of such defense spending--absent this spending occurring, would the government allocate the expenditures to another program or reduce expenditures overall and how would that affect the median income of an American worker?
One concept that is not perfect but has some proponents is the "fiscal multiplier", which is essentially the estimated ratio of money spent on some government policy to the amount increase in nominal GDP (or GNI). There is a plethora of economic literature on comparing the fiscal multiplier of different policies under all kinds of assumptions, but almost all the time in the current context, direct cash transfers to the lower classes tends to have the highest multiplier.
In general as a biased observer, I would say it's easy to say overall that the GWB admin, including the billions spent regarding Afghanistan and Iraq, had an overall worse outcome on the vast majority of Americans, and that alternative policies would have done better, but isolating the effects of defense appropriations across the income/demographic spectra of the populace is something difficult to answer. There are probably some smart people somewhere that have done the research to find some semblance of conclusions there though.
The concept of the 'fiscal multiplier' is Keynesian demand side economics. As a neoclassical supply side economics adherent, I disagree that, in the long run, there is any 'fiscal multiplier' except when the economy is not operating at full potential output (full employment.) I.E during a recession.
However, I agree that in the short run, government deficit spending does stimulate the economy (as occurred under President Reagan, President W. Bush and President Trump.)
The part I think you left out is the borrowing costs required to finance either the spending or the tax cuts (which was most of the form of the stimulus with Reagan, Bush and Trump) which can 'crowd out' non government borrowing by ultimately being inflationary and reducing the generally more sustainable private sector borrowing (as we saw at the end of the Reagan Administration, the Bush Administration starting in 2006 before the rise of oil prices and, to some degree, the Biden Administration in 2022.) As Milton Friedman said "the long run fiscal multiplier is dead."
However, there is a time lag between the government stimulus and any negative consequences to the economy