I have seen AA shoot down aircraft, but it's very rare. In the "Road to Bastogne" (Fuhrer Begleit Brigade) campaign I managed to shoot down 3 or 4 in the span of the campaign. Considering you get up to a dozen or so AA in some battles it's still not a good total and most of the time you miss or manage to drive them off for that run if you're lucky. That said, when you know the opposing side has aircraft, it's usually another episode of that game show skit "How not to be seen" an hope the aircraft don't find you anyways.
Now, I will admit that seeing a dozen flak open up & shoot into the sky is pretty cool to watch, and if they do hit the plane, the crash is VERY satisfying...
Jyri