No, because you can stall a wing at any attitude realtive to the horizon. It isn't about the pitch of the airplane, it's about the relative airflow over the wings.

So if you're falling quickly the airflow comes from "below" which causes a high angle of attack even if the nose is pointing level compared to the horizon.

That's a very interesting thought. How would you do it? You can only sense the acceleration - if it's lower than 1G you're falling. The angular momentum doesn't actually tell you anything in an aircraft.

I wonder if it's possible to estimate the local air speed based on ground speed (GPS) and local weather data (can we measure wind speed at altitude?).

I'm doubtful. Consider this: the aircraft can experience a downward acceleration (eg. due to turbulences) without being in a stall. Measuring the AoA is still the most reliable way (assuming the sensor itself is reliable) to detect impeding stall.