Good questionWow, just saw this - incredible find, if it's an original (or, frankly, even if it's a reproduction - getting a GW, BK or Aero for pocket change? Unbelievable!).
I'm probably completely wrong here (and if I am, I'm looking forward to learning more!), but...shouldn't an original A-2 jacket have a leather nameplate? And some sort of decal on the left shoulder indicating the affiliation of the pilot? And maybe rank insignia on the shoulder straps? Or at least traces to show some of those things were originally there? Were there WW2 pilots that had "blank" A-2s? I'm genuinely curious about this.
Great find no matter it's origin!
The short answer is that yes many USAAF people wore jackets without name tags or the Roundel on the shoulders. You can find photos of them all over the photo section of this forum.