No. A new vault is a freshly generated 12-word recovery phrase, nothing else. No email, no username, no phone number, no verification step. If you sign in with the phrase, we could not email you even if we wanted to, because we never learn who you are.
Prefer a familiar flow? Sign in with Google, Apple, or GitHub works too. That route necessarily tells us the email tied to your provider account, but your notes stay end-to-end encrypted either way, and you still get a phrase under the hood.