This is a super interesting question. Off-hand, I am having trouble finding much on this (as you mention), and what I have read pertaining to Aboriginals in relation to this era of military history has more to do with the effects Aboriginal involvement in the World Wars had on the politics post-war. I will tackle what I can from a Canadian context (though with reference to Vine Deloria Jr., who is an American Indian), however, though hopefully someone more capable can give a much better write-up.

On how Aboriginals might have reacted to Nazism, let's start a bit later and refer to Robert Alexander Innes' article "I'm on Home Ground Now. I'm Safe": Saskatchewan Aboriginal Veterans in the Immediate Postwar Years, 1945-1946 (from American Indian Quarterly Vol. 28, No. 3/4, Special Issue: The Recovery of Indigenous Knowledge (Summer - Autumn, 2004), pp. 685-718):

After the war the newspapers made Canadians aware of the Indians' substandard living conditions. Canadians recognized that the treatment of Indians disconcertingly resembled the treatment of minorities in Nazi Germany. (p. 705)

And a quick glance at Vine Deloria Jr.'s God is Red (30th Anniversary Edition) writes (concerning the American context):

During World War II a large number of Indians came to the west coast to work in war industries, and after the war they were shunted aside as returning white veterans were given back their jobs.... In almost every part of the nation, Indians were treated with disgust and disdain by the whites of their region. (p. 3)

Vine Deloria's book mostly deals with Aboriginal spirituality in philosophical terms, but his attempt is grounded in his understanding of history. In general Vine Deloria Jr. paints the older generation of his day (writing in 1973, when he himself was 40) as complacent, but not ignorant -- as a persecuted people they don't want to risk what few privileges they do have by being confrontational. Deloria pretty consistently draws upon World War II and the Nuremberg trials as showing the hypocrisy of American treatment of Aboriginals (in his Metaphysics of Modern Existence he makes the claim that the racist ideologies of America were no different than Nazism). Deloria's portrait seems to suggest that Aboriginals would have made the same linkage that Innes claims Canadians are making post-war. For Aboriginals, Nazism might have been a different face to the same old white supremacy.

But another question, one that adds wrinkles to the broad strokes of Deloria, is how loyal can we assume Aboriginals were to the nation-states they found themselves in? From A Concise History of Canada's First Nations: Second Edition (by Olivia Patricia Dickinson w/ William Newbigging):

At this time, and even though they were not citizens, Amerindians were serving in the armed forced during World War II in proportionately higher numbers... than did any other segment of the general population, repeating a pattern that had been evident during World War I. (p. 248)

I don't know if the amount of American Indians in the service during the World Wars were also notable, but if they were it suggests that perhaps Hitler had not done his research as to whether or not there was the will to destablize the regimes. Deloria's sketch of the older generation during the 1970s suggests that there might not have been much of a will; during the American Indian Movement such radical views might have been more common, but I suspect that the his portrait of an older generation that wants to just survive and not risk the ire of the government is not too far off.

Also, Innes deals with the high number of Aboriginal military serviceman and suggests that there might have been greater conscription in the reserves than is typically assumed -- while conscription in some treaty territories did stop, previously conscripted soldiers from these areas would have been forced to serve despite that. But he also notes that there does not seem to be evidence that the Aboriginals deserted in any notable numbers (likewise the image of the Aboriginal Canadians after the war is elevated precisely because they have been stereotyped as very capable soldiers). But it does illustrate that it is hard to determine how they perceived their military service or themselves in relation to the nation-state.

Anecdotally, I do know Canadian Aboriginals who had family serve in the military. In that small sample, loyalty to treaty relationships (even if, in actuality, these treaties have continually been broken by whites) is a possible motivating factor to enlist -- there is a treaty with the crown and you should help your allies. But for others there's also self-interest at play -- service can involve enfranchisement or just the hope for better living conditions (with the hope of being able to get a better job after your service). But the important part there, as it pertains to this specific question, is that there might have been a sense of loyalty to the crown in Canadian First Nations -- whether or not American Indians would have the same sense of loyalty is hard to say.

If there's a point to be drawn here, I think it's that it's tough to say that Aboriginals would have found a perceived ally in the Nazis. Some might not have seen them as any different from the bigots with German last names they already had to deal with when they left the reserve. Some would have loyalty to the British crown due to their past treaties (and perhaps some would feel sympathies to the French state for similar reasons?). And some would probably have a hard time being too concerned about European powers fighting amongst themselves.

Just a heads up, the link on your post is broken.

Follow up: Does it relate at all to the work of Karl May and the subsequent German fascination with Native Americans that has somehow persisted through all the turmoil that Germany experienced in the 20th century?

Follow up question: In Mein Kampf, Hitler compared American segregation and the one drop rule favorably to Latin America, where he said race mixing led to a lower level of civilization. On the other hand, he claimed the salient characteristic of Aryans was their willingness to fight and die on behalf of their race. Can what he wrote in Mein Kampf be reconciled with the above equivalency of Native Americans with Aryans? Or were these sentiments merely fanciful and insincere?