Oliver Stone's documentary "South of the Border" apparently includes this account of the former Argentine president Kirchner about a conversation with GWB:
It's not exactly uncommon that people believe in positive economic effects of warfare, but those effects are mostly illusions, caused by tunnel vision.
In the realm of macroeconomics, expenditures for warfare are about equal to expenditures for a program to build buildings, then blow them up, build again, blow them up, ... it's consumption that does not stimulate anything and doesn't meet the consumption preferences of the population.
Investments usually increase the economic output (depending on circumstances), while additional consumption does so at most by a factor of 1 unless the economy was running at significantly less than full potential (and only if the circumstances allow it).
A war can of course erase unemployment, but keep in mind that all the mobilised soldiers don't really "work" in the economy during war. They're the equivalent of unemployed people, adding nothing to the nation's economic output.
There is one valuable thing in war, though: War - and especially the emotional mobilisation of the population by it - can provide motivation, break up resistances and such. Re-distribution fo income becomes fairly easy during war.
Motivation is the key in every economy, it drives them. It's what comes before the worker even raises his hand. A very detailed research into the motivation effects on the micro and macro scale could consume the whole career of hundreds of economists, and economists tend to be more interested in researching peacetime economies.
It's therefore difficult to tell what exactly changes due to the changes in motivation, but it's quite safe to say that these effects do not apply significantly to peacetime military spending.
Even IF the motivation of the population in wartime would change enough to enable a net positive economic effect; that effect would not mean that peacetime military spending could be considered as an economic advantage. It's simply a form of government consumption actually.
There are additional reasons why a look at the economic effects is almost excessively difficult; most wars are short. It's possible in wartime to postpone the replacement of old machinery and buildings, for example. These investments are a huge factor in normal, peacetime economies. You can postpone them - which merely postpones investments and frees production potential for other production.
There's also the problem of waste. The GDP metric is generally under fire for being a poor indicator for welfare. To raise a building and then blow it up does increase economic output just as two neighbours helping each other does not while them doing the same and paying each other an identical sum does.
The welfare effect of economic output isn't shown in GDP. The GDP merely shows the extent of official economic activity.
The economic activity of warfare has very little to do with welfare (private consumption drops significantly in major wars), and even worse - much of the war expenses are usually wasted. Again, this waste is not being subtracted from the GDP.
In short; even if (and that's not for sure) warfare does increase the GDP on paper, it's among the most crappy tools for economic recovery. High peacetime military spending is similarly crappy for the purpose.
Then again, it's not surprising or even unbelievable that GWB recommended war as economic policy.