The answer
No. Offline private keys protect signing access; blockchain visibility depends on the chain and address history.
What to do next
Use separate addresses and understand on-chain privacy instead of assuming cold means anonymous.
Trezor hardware wallets
Potential cold-storage product; not a substitute for safe backup procedures. Availability, supported assets and local eligibility must be checked before signing up or buying.
Visit Trezor hardware wallets ↗Official provider link · Compare suitability and availability before choosing.