What happens if no CertificateVerify is sent in TLS?

I know in TLS, the client would send a CertificateVerify message for the server to confirm the client’s identity through means such as CA but what if the client never sent this information?

Is it possible for an attacker to use this opportunity to hijack the client’s session through packet sniffing and create it’s own "pre-master secret" to communicate with the server?