I don’t think there has been any F-22s in range of their AWACS.
They don't need an F-22 to make the claim - they need to be able to detect a target the size of a bird at 200 kilometers - and today that's pretty close. This still would not do much to harm the Raptor. It would still be nearly impossible for fighters or AA missiles to see it. It's never been claimed (except by reporters) that the Raptor is invisible to radar - just that it is very hard to detect.
If this AWACS can detect it, can it not provide guidance to any missile aimed at the F-22?
Maybe a newly hatched hummingbird. The trouble with such a system, even if feasible (and I doubt the power output ability), is that it would have to have such a low threshold that it would process everything (how many birds within 200 kilometers?). No problem, it could then set a Doppler filter, which is normal, but the weakest of signals would fool it. We could literally provide it with hundreds of incoming F-22 signatures. Electronic warfare is generally coupled with stealth, because stealth makes spoofing so much easier.