There's reasons to think that a Keynesian program (even one which focused on war, not building useful infrastructure) could have ended up fixing a truly out-of-kilter economy.
But it only fixes medium term (~10 year horizon) problems. Once the monetary / investment system is fixed, Germany would have stalled. It suffered from massive brain drain (if you literally have Einstein, making him flee isn't a great idea). And totalitarianism isn't great for creating an innovative workforce, even if you can keep your population from fleeing.
If you are embarking on such a Keynesian program in a climate of general depression and lack of investment in other countries then you will enjoy generally low interest rates but you lose the ability to make short term investments and must make longer term ones.
In the case of Nazi Germany Hitler purposely took on massive amounts of debt to rearm the country. Any economic success was temporary and entirely dependent on the massive arms program. Not only was the Nazi state inefficient arms investment couldn't possibly have ever paid back the investment in borrowed money that created the Nazi military.
But it only fixes medium term (~10 year horizon) problems. Once the monetary / investment system is fixed, Germany would have stalled. It suffered from massive brain drain (if you literally have Einstein, making him flee isn't a great idea). And totalitarianism isn't great for creating an innovative workforce, even if you can keep your population from fleeing.