@mensa73 - A Google search for "National Jewish Welfare Board" located the finding aid document relatively quickly.
There are a number of references in the document to records of non-Jewish servicemen. There is also this statement, in the description of Series VI:
"The BWR transcribed information on the master card forms using several encoding schema. In one encoding scheme, labeled the Master Card Symbols, ... punched a hole in the card to indicated that a soldier is not Jewish; stamped the word "authenticated" in a box if the information is verified"
On Pvt. Besch's card, there is what could very well be a punched hole at the upper left.