Airpods Pro 2 won't connect if case's batery is dead.

Can the AirPods Pro gen 2 connect to my iPhone if the case's battery is depleted even if each AirPod has 100% battery?

I find it weird that the AirPods have 100% battery, but when the case's battery is dead, the Airpods won't connect to my phone. Is this normal?

Thank you!