Does the AirPod Case, or headphones when in the case, emit a bluetooth ID? I'm concerned about privacy and don't want my airpods (or the case) to emit the bluetooth ID while I'm shopping in malls that use iBeacon technology.

How can I be sure that the airpods (when stored in the case), and the case itself doesn't leak out a Bluetooth ID while I roam?
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.