Does the AirPod Case, or headphones when in the case, emit a bluetooth ID?
When the case is closed with both AirPods inside, you can't locate the AirPods. It will only show the last know location which is when the AirPods were last connected to a paired device. So no Bluetooth is not emitting if the AirPods are in a case. Technically they are turned off.

If you want to test them you can place them in a case and then check for bluetooth signal or go to find my iPhone and see if you can locate them. It will only give last known location.