If I am correct, it is one of the first episodes of the first season. The scene in which I refer is where Lt. Speir's is giving German PoW's cigarettes, then all you hear in the next scene is Thompson gun fire.
Edit: minor, grammatical error
The best video of the scene I could find there is a weird cut 20 seconds in, which skips part of the scene where the guy says he's from Oregon. It is later on Band of Brothers Episode 2, "Day of days"
I don't have an answer to your question, but per the episode you cited, here's the relevant dialog:
Malarkey: Why are you in a Kraut uniform?
Anonymous soldier: Volksdeutsche.
Malarkey: Come again?
Anonymous soldier: My family answered the call. All true Aryans should return to the Fatherland.
So that might give you some reference on what to explore further (Volksdeutsche).
The short answer is yes, there were schemes to encourage ethnic Germans living overseas to return to Germany.
One such program was the Rueckwanderer, by which overseas ethnic Germans could go to their consulate, swear allegiance to Germany and state their intention to return to the Fatherland, and got access to a special currency that they could purchase at a favorable rate but could only be spent in Germany itself. This was a double win for the Nazis, since they got foreign currency (of which they had a critical shortage - see Tooze's Wages of Destruction) as well as their precious German.
Another example is the Waffen-SS formations composed of foreign-born ethnic Germans, or Volksdeutsche. These were initially volunteer units, but conscription of male Volksdeutsche of military age was imposed in some German-occupied areas from 1942. Had the SS completed their programs, these men and their families would have been eligible for settlement in agricultural colonies in the newly annexed and depopulated regions. See Lumsden's SS: Himmler's Black Order 1923-1945 and Hale's Hitler's Foreign Executioners.
Follow up, if this did actually happen, what happened to them post war? Surely this would constitute treason?
Piggyback question, would this be considered treason to the United States government?
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