I think you didn't yet fully understand how bitcoin (or crypto in general) works.

Your coins are not stored on your wallet. Your coins are assigned to you on the blockchain.
With the corresponding private key (which is stored in your wallet), you are then able to control them.

All you need to control the BTC are the private keys. And these private keys are derived from the mnemonic code (the 12/24 words).
Anyone with access to these keys can access your coins. There is no need to connect anything to "the blockchain".