The answer
No. Encrypted storage can protect secret material at rest, but Bitcoin spending signatures remain governed by Bitcoin protocol rules. Quantum-resistant encryption does not change the on-chain signature algorithm.
What to do next
Treat storage encryption and blockchain signature migration as separate protections.
NIST post-quantum cryptography
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Trezor hardware wallet
A current-generation hardware wallet for managing keys; it does not make Bitcoin or Ethereum quantum-resistant or resolve a future protocol migration.
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Frequently asked questions
Does a hardware wallet need a protocol upgrade to sign with a new algorithm?
It needs compatible software and the blockchain must also accept the new signature mechanism.