

American culture was a major export during the Great Depression, so it is likely that American culture would continue to be an export unless the USA ceased to exist.
I would just expect Nazi Germany to censor and control some of America’s cultural exports. Hitler liked Disney movies, for instance. However, jazz was banned.
And the USA has significantly intervened in Middle East politics.
It is likely that Nazi Germany would intervene in the Middle East to secure its oil; the various nation-states were still forming and borders were somewhat volatile. Germany would likely intervene to ensure that the oil flows.
Also, after a while, the German state would need another infusion of money and cheap Arab oil would be a perfect resource to bring under control of the Nazi state.