Dan, it would not surprise me at all, if there were a small number of persons during the war, who were indeed Muslims, or, as they preferred to call it, at that time "Mohammedans". During my research on the personnel of the Navies and other related subjects, I did come across mention of this fact.
One such mention was in a newspaper report (don't have the exact details at the moment, but can get my hands on it, at a later stage, if needed) about a soldier in the United States Colored Troops, who had been born in the Middle East, and was originally a "Mohammedan", but, in his travels, finally ending up in the U.S., he was converted to Christianity. I also have the names of a couple or more soldiers which are definitely Muslim or Middle Eastern sounding.