Luftwaffe and Airborne off-map "attacks" are atleast possible to shoot down with AA.
Except not really. Planes are nearly impossible to shoot down, the only thing that works effectively is a lucky shot from an 88 (lucky because it has to hit), and the 88 can't be targeting anything else, and it has to be coming from a certain distance otherwise the 88 cannot raise its elevation fast enough. Ostwinds, Wirbelwinds, Flakvierlings, Pumas, Armoured Cars, Quad 50mms, and Bofors 40mm all struggle to actually bring down the plane even though they shoot at them.
In addition, shooting down planes often has little effect. Recon planes still get good recon in, strafes finish firing far before they get shot down, Panzerknackers will fire far before they get shot down and there are multiple of them. And every plane luckily shot down has a chance to crash into something of yours causing massive damage.
Just for the sake of wasting time, the effectiveness of various weapons vs. aircraft:
Quad .50cal: 0x pen modifier, never kills
40mm Bofors- 150%! accuracy, about five shots to kill
88mm FlaK - 33% accuracy, one shot kill
20mm AC/Puma - 15% accuracy, five or six hits to kill
20mm Quad (FlaK) - 10% accuracy, five or six hits to kill
20mm Quad (Wirbelwind) - 35% accuracy, two to three hits
37mm Ostwind - 35% accuracy, three hits to kill
(It turns out Bofors are actually quite useful here, but ssshhh)