In the real world the Nazi's didn't have a problem using convoluted logic to include others that you would think would be excluded if it was politically expedient. The alliance with Japan being the most obvious example. The Nazis would be free to turn on these groups when their usefulness had been exhausted.
You were right in both respects - that the Nazis allied with Japan during WW2 and that they would have turned on them eventually. Hypothetically speaking, however, there would've been no reason for the Reich to ally itself with a secret society of assassins (such a small group, even if the membership was in the thousands), unless the Fuhrer saw an opportunity to profit from the League.
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