Nope. It was a German Romantic concept.
A product of the Enlightenment, not the old order.
They are cousins, yes, but Nazism's wellspring was the conservative-nationalist base.
Again, I disagree. The monarchists and the Centrum were the German conservatives. Some nationalists were conservatives and some were socialists.
Nazism was predicated on two ideas: scientific racism and secular statism.
Scientific racism is a leftist innovation of the Enlightenment as is secular statism.
A true German-speaking conservative in the 1920s/1930s could be of two varieties: a devout Lutheran supporter of the Hohenzollern dynasty and its junker class or a devout Catholic supporter of the Habsburg dynasty (in Austria-Hungary) or of the Centrum (in Germany).
These were precisely the kind of men who populated the Third Reich's army officer corps at the beginning - which is why the SS was created as a counterweight to what Hitler himself described as "reactionaries" in the Wehrmacht.
It was conservatives such as these who plotted against Hitler's life and almost suceeded. Claus von Stauffenberg was an almost perfect example of an actual German conservative, as opposed to a typical Nazi leftist.
Many things were products of the Enlightenment, not all were left wing developments. When I say VG was a popular idea among conservative elements, it only means that it found traction among traditionalists (however idealized the past) and not the Social Democrats or Communists.
I'd also argue that Nazism borrowed elements from scientific racism and Social Darwinism but there was a strong and mystical neo-pagan element to it. There is a difference between Hitler's racial vision of history and the world and scientific racism. A vast difference. Jews as the parasites and the antithesis to the true civilization of the Aryans was on the order of eschatological religion.
It's not that Nazism didn't have leftist threads, considering that era saw an increased rejection of liberal societies in favor of secular statism, based on some communist utopia or a harmonious, classless "Volk."