Indeed, it works I keep my CBT plugged into my Mazda even tho I wont drive it for weeks at a time. You just need to enable the 'Naptime' middleware.
In a lot of cars you will find a kind of heartbeat message. It's dispatched maybe once a second while the car is on. You can pass this message id into the middleware and it will automatically go to sleep when it does not see it for a while. It also sets a filter on the CAN controller that will trigger an interrupt to wake the system back up when it does receive the heartbeat message.
Here you will see it's enabled by setting a C def:
You can just uncomment the def on line 16 to enable the Naptime middleware. And be sure to set a heartbeat message id on line 56 or set it to 0x0000.