From what I know, yes, that was an aspect of Nazi ideology. I'm afraid I can't give too detailed a response as it's been ages since I've read the book I'm sourcing and I don't actually have the book on hand, but I'll give it a fair shake.

The line of reasoning behind the thinking of the German's here goes back to a book written by Tacitus, a Roman writer in the 1st Century C.E., called Germania. In it, he spoke very highly of the German barbarians tribes, but this was honestly more of a way of critiquing the Romans living at the time, who Tacitus did not think much of. In addition, Germania was written from an outsider who I do not believe spoke their language or possibly had even visited the area (please correct me if I'm wrong), so his knowledge of what he was talking about is questionable.

Still, the idea was there that these German tribes were of some kind of superiority, and over the centuries Tacitus' Germania became something of a symbol of German nationalism. This is never minding the fact that the German tribes of Tacitus' day got shuffled about in the ensuing centuries and weren't more direct ancestors to the Germans than they were to, let's say, the French. Still, the Nazi's do love German Nationalism, so Germania would have fit quite nicely into their propaganda efforts. To quote Tacitus:

For myself, I concur in opinion with such as suppose the people of Germany never to have mingled by inter-marriages with other nations, but to have remained a people pure, and independent, and resembling none but themselves. Hence amongst such a mighty multitude of men, the same make and form is found in all, eyes stern and blue, yellow hair, huge bodies, but vigorous only in the first onset. Of pains and labour they are not equally patient, nor can they at all endure thrift and heat. To bear hunger and cold they are hardened by their climate and soil.

Sound familiar? This was enough to get Himmler to make an attempt to get his hands on a very early copy of the manuscript.

I'm reading now as I research this a little that the book I'm looking to site, A Most Dangerous Book by Christopher B. Krebs is somewhat controversial in the academic world, so take all this for what you will. I think that there is evidence for Nazi's using the legacy of Rome in there propaganda here, but I'm afraid not being a serious scholar on the subject I can't say any more. I can also not speak to German-Italian relations as a result of it.