The auto trim stops long before the stall bloggsie. If they let go of the stick at the first stall warning (or any time really) the aircraft would have stabilised at the trimmed airspeed out of the stall (letting go too long after entering the stall may mean you run out of air to recover in...bugg@). Well that's what would happen in ALTN law. In direct law this would happen unless you push the motors up to the full noise position, in which case you may run out of stick authority (depending on how slow you got), in which case you need to go to idle, and maybe roll to get the nose down. Pretty conventional really.
To stall an Airbus you need to hold back pressure on the stick to maintain an attitude once the autotrim stops (autotrim will work into VLS, but stops prior to Alpha Prot or Alpha SW, depending in what law you are in). This is a big warning sign of what is about to happen if you continue doing what you are doing. Seems easy sitting at a desk, but add fear, startle effect, and pilots that have only experienced non-normal in a Simulator and the outcome will not always be successful, as shown by bent metal of all makes.