It would've still stopped - the FSD system doesn't override the background tasks that power the AEB systems that stop the car from hitting humans or cars.
We also don't know the opposite but that sure as heck won't stop people claiming they know it as a fact and cause the publication of dozens of news articles over nothing.
Imagine AI puts you into a separated oncoming traffic lane when visibility is extremely low (a few meters) and then disengages. It might take you quite a while to get out of such conundrum.
Unless you are referring to these [0] incidents from 2016, before FSD was released. That was Tesla Autopilot (which comes standard on all Tesla vehicles now).
Also, FSD uses active camera monitoring to make sure the driver is paying attention, so no you can't sleep in your while FSD is activated.
AEB cannot magically instantaneously stop a car that FSD has put into the wrong lane. If you believe otherwise, please do not drive. Cars are dangerous in the hands of those who do not take risks seriously.
At this point I can't imagine buying anything Tesla related. Or anything related to Elon Musk for that matter. He's a grifter who has managed to stand on the shoulders of giants and call himself tall.
We don’t know that. An Tesla cannot claim it.