At alpha max (AoA protection) you will go down, if no additional power is added. But going down does not mean stall. Alpha floor has indeed nothing to do with this. It is just another feature that prevent the a/c from stalling, but only when A/THR is operational.
Conclusion indeed is: In normal law you will have AoA protection that will prevent the a/c from excessive AoA (stalling). This does not mean it prevent it from descending or from being slammed into the ground due to WS, or whatever senario you would like to create. For that you still need pilots input.