Whether its barebow or
recurve would depend on whether the string rests on the back of the bow or not after the tip. there was a discussion about flatbows and which catagory they came under thats got me thinking this. But your probably barebow.
Sorry, this makes no sense at all. #
1st The string lies along the belly, the back of the bow is the part of the bow facing away from the archer when the bow is being shot. I think what you mean is that it will be an American Flatbow if the string only touches the bow at the nocks, and doesn't lay down the belly (inside) of the limb.
2nd It doesn't matter where the string is for GNAS target it will be barebow. For GNAS field as woodsplitter said, it's either Trad or barebow depending on arrows and technique used.