I guess it is not ok to be asleep as even a loud alarm will take time to wake you up, but not paying attention, like when you are doing your email is fine. In fact, that's the entire point of level 3 autonomy.

You are "on call" rather than "at work", so you must be prepared to act when the car rings. If the car doesn't ring, you are free to do whatever you want as long as you can hear the ring and take back control when it happens.