For those who haven't seen BoB: http://www.youtube.com/watch?v=HQv0_1X5Ua8
I just want to preface before answering this question, that this is a very difficult question for me to answer, in that my research of the subject (and it's something I've been curious about/researching since seeing that scene you mention originally air 13 years ago) has turned up very little about any hard numbers of American citizens who fought for Germany during WWII, nor has it turned up many primary or (reputable) secondary sources that focus on the question at hand. It also doesn't help that the majority of information/sources I come across is either anecdotal or tertiary sources (and also vague on what source it's reliant upon). One day if I ever end up getting another degree in history and I can get a grant to go dig around in some German archives, I think this would make one hell of a dissertation but until then, I'll make due and answer your question to the best of my ability. It's also possible someone else here is aware of a source that I'm not and is able to enlighten us all on this subject, which would be welcome.
With that said, onward with an answer.
I am going to get the hard part out of the way so I don't get any hopes up as I go along. So far as I can tell, no hard number exists in regards to the number of American citizens (either by birth or naturalization) who fought for Nazi Germany. This is somewhat explainable for a few reasons. One being the fact that in regards to German military KIA/MIA's, the large majority of those losses occurred in the Eastern Theater, and it's likely that the Soviet's cared far less about the immigration status of a German solider they had killed/captured who had lived in America for a few years than the Western Allies would if that discovery were made. It's also more plausible that that soldiers citizenship history isn't necessarily provided or proved in any useful way if they are killed in combat. Also one other major factor to remember, is that German records detailing a particular soldiers immigration and subsequent repatriation may not have survived the war. It's especially hard to narrow down where people (especially in Germany and Eastern Europe) ended up from where they were at the beginning of the war.
As far as German soldiers on the Western Front who were American Citizens, Donald Malarkey (The American para in that scene is based off of him) has recollected both since returning from service and since the show has aired that this incident did take place. Beyond that, I am unable to find any further proof of this (neither the German-American soldiers identity can be ascertained, nor can I find an after-action report that might corroborate the story) and that's unfortunate, because while I honestly believe the exchange took place, it's hardly something that can be used as a sole historical source for reasons we go over in this sub from time to time.
Now, there were certainly cases of Germans who had immigrated to America (as that scene from Band of Brothers describes) and then returned to Germany at some point before the War broke out. The issue here is that unless they specifically were sought out by the Allied powers at the end of the War (and the British for instance, who had a small number of their citizens volunteer for Germany as well, were very diligent in finding those citizens that did), it's unlikely their status as either naturalized or born citizens of America would come back to haunt them unless they A) were guilty of war crimes or B) re-immigrated back to America and had to account for where they were and what they were doing during the war.
Here is where it gets interesting. There are a few rarer cases of Americans who actively sought out to assist or join the Nazi cause in a military capacity during the war. Oddly enough, not much has been written about either person. The most famous (and by famous I mean, the one who was subsequently tried for treason) is Martin James Monti.
Monti was a 2nd Lieutenant in the U.S. Army Air Corps who was stationed in Karachi, Pakistan (India at the time) in 1944. He eventually went AWOL, made his way to Cario, Egypt and managed to take a reconnaissance P-38 and flew to Milan where he surrendered himself to the Germans. Monti then joined the Waffen-SS and helped assist them with propaganda efforts primarily aimed at American POW's and allied soldiers fighting in Italy, under the alias "Martin Wiethaupt".
Eventually Monti deserted the SS, made his way south towards Allied lines and surrendered in his SS uniform, which he claimed was given to him by partisans so that he could "escape" captivity. He then claimed he was initially captured because he was shot down while conducting an unauthorized air-raid on enemy forces. He was subsequently court martialed for desertion (at the time, the Allies had no idea about his collaboration with German forces) and sentenced to 15 years hard labor. He then had his sentence pardon a year later based on the condition that he rejoin the army. He did so, attained the rank of Sergeant, but was then arrested by the FBI in 1948 on charges of treason, as his identity of "Martin Wiethaupt" had come to light. He was subsequently sentenced to 25 years, but was paroled in 1960. He died in 2000, but beyond that I am unable to find any further information on him. Here is a collection of NY Times articles detailing his trial, sentencing, and the events that led up to them.
The two other names that I've seen pop up (and this is excluding cases like "Axis Sally" aka Mildred Gillars) is Peter Delaney and Fred Konig. Delaney supposedly facilitated Monti's entry into the SS (but I've yet to see any source that confirms this) and was killed during an air raid in 1945. Information on Konig is light, and the only source I can find is this website, which does not provide any source citations or copies of the primary documents that author used to arrive to their conclusions, so you need to be extra careful taking anything said there as fact.
Beyond this, there isn't much out there that I have been able to find on this subject, but I hope the small bits I've provided help provide you with somewhat of an answer.
[This] (http://www.reddit.com/r/AskHistorians/comments/1f43i8/in_the_series_band_of_brothers_during_the_post/) thread might be of use to you.