It requires some sort of connection to the phone network or internet, and the ability to run code sent to it by the attacker. It can‘t do either of those while it is powered off. All of your accounts linked to your phone will be online, and they can still be hacked even when your phone is off.
When you call a dead phone does it ring?
Answer: A: With a dead battery it should not ring but it should go to voicemail directly.