Yes, you can transfer offline and keep the value in the vault but the main difference is that you can resend any instrument you receive offline without a connection.

Eventually as with all bitcoin transactions if you need to go back on chain the broadcast and signing needs to be online for that to be final. You can batch instruments to save on mining fees when you do go back online.

bitcoin

Kagikai:  Zero Fee Bitcoin Bearer Instruments in Hardware Security Enclaves

kagikai

Yes, you can transfer offline and keep the value in the vault but the main difference is that you can resend any instrument you receive offline without a connection.

Eventually as with all bitcoin transactions if you need to go back on chain the broadcast and signing needs to be online for that to be final. You can batch instruments to save on mining fees when you do go back online.