This is a really good question and kind of goes in line with my thesis. Even though it's 1812 vs. 1940, it's a question Americans have dealt with for our entire history. Don't forget the Americans who fought in the Spanish Civil War in the 1930s.
There may be, but if not, there should be, a book tracing American views on this throughout time. In 1794, we passed the Neutrality Act, to prevent privateers from serving for England or France during the Napoleonic Wars, but this was flouted often. Other nations had similar laws. Just finished a book on Confederate Raiders and England had a "Foreign Enlistment Act" meant to deter this kind of thing, but their leaders often looked the other way. A lot of times, these laws are only on the books to provide the veneer of government disapproval for the sake of plausible deniability.