By chance do you have any other device (firefox, chrome, android, ios, etc) that might be logged into your vault? If so, disconnect the device from the Internet before doing anything. Then unlock the vault, grab your recovery code, TOTP secret, backup password, etc. and put them on an emergency sheet. Only after you have everything else recovered should that device be reattached to the Internet.
Unless you have a syncing relationship pre-established with bitwarden authenticator, the answer is no.
You might also review this document for some hints.