How much truth is there to the claim that if Nazi Germany hadn't waged war around 1939, its economy would've collapsed shortly after?

Very much. It was even publicly know among the allies that the German economy would collapse (or at the very least lead to a serious economic downturn) even if they went to war in -39. However, that prediction kind of rested on Germany not completely capturing France and Poland which gave them additional means. In either case, this particular topic has been written about before by me here and in the FAQ-section here.