Status of Eagle Squadron Pilots

For the first time in many years I watched 633 Squadron on the telly on saturday afternoon, oh dear, apart from the mosquito’s, I had forgotten what a terrible film it was.
However, I digress, as I noticed that Cliff Robertson was wearing an Eagle Squadron patch on his arm, although surely to late in the war to have been in existance then, it raised a question.
When US pilots were flying in the RAF prior to their official entry into the war, what happened to them when or if they were shot down and captured by the Germans. Were they treated as POW’s and put in with other captured airmen, were they deported to a neutral country as official non-combatants, the Germans presumably, not wishing to upset American public opinion, or were they shot as spies.
I know that some USAAF airmen flew ‘unofficial’ missions before December 7th 1941 in aircraft that came over from the States, the early B-17’s spring to mind.
Did these aircrew wear USAAF uniforms or were they kitted out as RAF personnel and were not officially allowed to fly over enemy territory, though from what I’ve read, some of them did, particularly late in 1941 when war for them looked a distinct possibility and they were learning European combat tactics. Were any captured and if so what happened to them.
Similarly, thinking of the executed Wermacht soldier in Band of Brothers, did any Americans return back to the home of their ancestors and fly with the Luftwaffe.