The latter half is maybe possible -- but when she leaves for work, I've been gone for an hour, miles down the road, phone and key with me.
Yeah. I guess it's that part where the behavior has to be verified.
We all know that "Auto Lock" when using a "Keycard" doesn't work; You're suppose to tap the pillar with your "Keycard" when you exit the vehicle to "Lock" the vehicle. "Auto Lock" is only a feature when "Phone as a Key" (Or maybe with the new Model 3 fob too since it supports Bluetooth) when the Model 3 detects the phone is no longer in the cabin and has moved out of range. Also, my assumption is your wife has no way to lock the vehicle after she exits. So, there's no way to lock the vehicle when she gets to work.
If the car is turned on or put into gear, specifically via the "Phone as a Key" method and not via the "Keycard", while the car is on and in gear and the phone is no longer detected (i.e. You're gone for hours, phone and key with you miles away), I don't think the car ever "shuts off"... Can probably test this theory by:
1. Get into car using "Phone as Key".
2. Put the car into gear and drive a bit.
3. Turn off Bluetooth on your phone or put into Airplane mode.
4. Stop and exit the vehicle. Close the door.
5. Wait some time... Maybe, not 9 hours.
6. Re-enter the door and see if the car is still on and allows you to drive off.
Again, this is just a theory.