Now it is often argued that making munitions (or digging ditches) puts money in the pockets of workers, who then spend the money back into the economy creating demand for the goods and services they consume. This is called the Broken Window Fallacy. Its true the workers will get paid and spend the money. But it ignores what the money would have been spend on and what effect that would have had if the government hadn't taxed it away from those who earned it. Others workers will not get the benefit of the lost spending power of the taxpayer.
As for conscripting workers... There's no denying slaves have capital value just like machines. That's not what you had in mind though.
Printing money is never helpful. It just transfers wealth through inflation from savers to the government. It's more beneficial to the economy to let savings remain in the economy. An efficient economy is one that maximizes consumers ability to have what they want to have and do what they want to do, given a scarce pool of resources. If the things government spends money on were economically efficient consumers would have chosen them in the first place so taxation and inflation (money printing) always reduce the efficiency of the economy.
My posts above do not say that a recession requires unemployment, and I am not disagreeing with your definitions as such. Let's stay focused on what we are in fact disputing here: either the economy grew during FDR's tenure, or it did not. From what I read, it did, regardless of his presidency, and I figure that at least some growth in the economy was as a practical matter virtually inevitable given how profound the contraction had been from late 1929 through early 1933. If you have facts to the contrary to show that it did not, feel free to offer correction.