Was the call explicitly for the war effort? How far in advance of the United States joining the war were people returning to Europe?
Here is a great response from a similar question a few years ago by u/coinsinmyrocket
<sets up lawn chair; good question!>
Follow up question: there are stories about numerous German POWs who were interned in camps in western Canada (I'm sure in the US too) who were leant out to farmers as general labourers to... well, replace the young men who went off to fight in Europe. There was little risk of escaping (2,000 miles from nowhere, speaking very poor English) and they were eventually accepted as part of the community such that after the war, and being repatriated to Germany, they rounded up their families and immigrated to Canada, the US.
For those American (or Canadian) Aryans who answered the call, I'd imagine the reception might be different. Any stories of such and how they were received (or not) returning from their war internment? Would they have been returned to Germany first, or could they just leave and go home to Eugene Oregon?
I can unfortunately not add further information about the subject matter to u/coinsinmyrocket's excellent answer here but I can add a couple of why this is so hard to find out and to some of the details of the presentation in BoB.
First on the difficulty of finding reliable source on any sort of number: We usually are aware of numbers and individuals of foreign volunteers in the Wehrmacht and Waffen-SS through information either supplied by these organizations themselves or via post-war trials in former occupied countries, which supply us with individual stories of people who went as volunteers. Recruitment in non-occupied and non-neutral countries was obviously illegal (I'll return to this point later) and thus we can say that most likely only a very small number of Americans joined the Wehrmacht or SS. Something that is further corroborated by the lack of many post-war trials in these countries. coinsinmyrocket mentions one concerning an American but as current scholarship stands that seems to be it.
This however also means that unlike in occupied countries, Wehrmacht and Waffen-SS files give very little detail on any sort of recruitment effort in GB and the US since, effectively, there wasn't one. Unlike, say, in Albania or the Netherlands or the Soviet Union where there were whole units of foreign volunteers and concerted recruitment drives, individuals from the US would not really show up in the documents of the leadership of these organizations. There are no seperate files on them like there are on the Skanderbeg Division or the Arab Free Legion, which were created with propaganda and recruitment effort in mind.
This lack of files leaves with but one possibility to ascertain the birth place if not nationality of members of the German Armed Forces – the Deutsche Dienststelle Wehrmachtsauskunftsstelle (WASt). Originally founded as an office to document the Wehrmacht's war losses in 1939 since 1945 it has grown to the foremost organization collecting Wehrmacht service records. In short, if you want to know about your relatives that served in the Wehrmacht, you write to WASt and they can and will supply you with at least the most basic information of their service record: Name, DoB, Place of Birth, Unit, Posting, Places served and if applicable, place of death and PoW time.
Now, you are thinking, this is easy, just request all the files of people born in the US. That seems like a good idea but it isn't possible. WASt is not an archive in the refulag sense, rather it is an agency with the specific purpose of supplying family members with information. That means in order to obtain information from WASt you have to have a name because they can not sort the data they have by place of birth. That is not their purpose, they don't exist for research, they exist as an information agency. So, in order to obtain the number and names of those Americans who served the Germans, it would be necessary to convince them to wave their rather strict privacy restriction and go through all their files identifying American-born Wehrmacht members. With 18 million Wehrmacht soldiers and most likely not more than 50 or so Americans serving in the Wehrmacht this is a task that would likely take you years of research.
Another detail from the aforementioned scene in BoB is that the soldier in the show spoke of "answering the call" for Volksdeutsche to join the Wehrmacht. This is most likely a throwaway reference but it points to another problem: Who would recruit Volksdeutsche in the US through propaganda and effort. The Nazi party had an ally in the US that served as their arm in the US, the German American Bund. Its first iteration already ended before the start of the war. Their leader Fritz Julius Kuhn was sentenced in 1939 to five years in prison for embezzlement and the Bund was in shambles. Later Bund leaders would not prove as effective as Kuhn had been.
The Bund did run draft evasion campaigns and was under intense legal scrutiny for it, specifically some of their leaders were prosecuted and Kuhn's successor had to flee to Mexico to avoid imprisonment. From their records, which are kept at NARA (RG 131) no propaganda material that called for Volksdetusche to go to Germany can be ascertained. So whatever call the POW from BoB answered, it was not an institutionalized one in the US.
Follow up: The part of my family that originally came over from Germany said they dropped customs, language, etc during WWI. If many German-American families had assimilated a generation previously, how prevalent was German-American specifically as a cultural identity in the 1940s? Were there still large blocks who hadn't yet assinilated, or were many of these newer immigrants?