Can I create an Unchained multisig vault using a singlesig hardware wallet that's currently in use?

Yes, you can create an Unchained vault even if you're using a hardware wallet for something else.

A singlesig wallet will have a specific set of addresses derived from its unique private key.
When creating a 2-of-3 multisig wallet, your hardware wallet’s public key will combine with the public key of two other hardware wallets to construct a new multisig wallet. The singlesig wallet is not even aware that it is also part of a multisig wallet.

Rest assured that the existing singlesig wallet funds will not be affected.