The answer is NO according to Larry White, one of the prominent Austrian monetary theorists and advocates of the free banking ideal.
Here is what Milton Friedman claimed they did, from Larry's paper:
I think the Austrian business-cycle theory has done the world a great dealof harm. If you go back to the 1930s, which is a key point, here you hadthe Austrians sitting in London, Hayek and Lionel Robbins, and saying you just have to let the bottom drop out of the world. You’ve just got to let it cure itself. You can’t do anything about it. You will only make it worse.… I think by encouraging that kind of do-nothing policy both in Britain and in the United States, they did harm.
What's the real culprit then?
Real Bills Doctrine.
Read Larry's paper here.