No, they serve a very specific purpose -- (attempting) to ensure the driver is at the controls and paying attention.

Don't confuse the FSD attention "nag" warnings with collision warnings. The collision warnings will sound all the time, with and without FSD enabled and even if you're not looking at the road. If you don't start slowing down quickly, Automatic Emergency Braking (AEB) will slam on the brakes and bring the car to a stop.

Heck, my car not only warns you, it slams on the brakes for you.

Scared the heck out of me when it happened, but it saved me from hitting something I didn't realize was so close.