Just tested it and no. If I locked the car with my key card, the doors would still open with the phone inside.
I didn't take the time necessary to let the car go into deep sleep nor did I wait long enough for the phone to go into any kind of sleep itself. I may test again with the phone not plugged in but I don't think that will make a difference. For me, anyway, I don't see the point. If I want to leave my phone in the car, I'll be more than happy to turn it completely off or put it in airplane mode; at the very least, turn off (not just suspend) bluetooth.