In particular if an attacker has a postgres superuser login they can essentially asct as the OS process owner, and could possibly get around the process hardening we already employ to reduce that risk, but again Vault is not designed to protect against a full superuser exploit. You must carefully guard database login access.
However, the secret data that is stored on disk, in WAL logs, and in database dumps is encrypted. This way you are ensured that your secrets are encrypted at rest. The Vault also provides using standard Postgres privilege access control (via GRANT/REVOKE) to control access to the decrypted data.