Note though that when your car is parked and shut down, and your phone is not paired with it, CarPlay is not active at all. CarPlay is nothing more than a software conduit to run iPhone apps on your cars display. CarPlay itself has no ability to detect location, transmit information or receive information other than through the iPhone. CarPlay is a purely passive pass-through for your iPhone apps. It is literally incapable of doing what you suggest it do.
For what you wish, your car would need its own independent location detection capability (e.g. GPS, if the car has a NAV system), and it's own independent wifi or cellular radio to connect to the Internet and transmit its location information to a tracking system.
The CarPlay software itself has none of that capability and cannot have such added as the required hardware would need to be built into the car.