Yes. They may or may not be able to access messages directly (i.e. Brute Force the encryption text, compromise WhatsApp itself, parter with WhatsApp, etc) but it’s almost a certainty if the government really wanted to at a minimum they could use some type of side channel attack.
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.