No. Domain locking only prevents you from modifying your name servers. Even when your domain is locked, you will be able to make changes to your other advanced DNS records, domain registration information, and more from your Domain Control Panel.
Please note that domain locking is available only for domains registered through Yahoo! after January 22, 2001 (or, for Merchant Solutions customers, after March 23, 2001). If you redelegated a domain you registered elsewhere for use with your Yahoo! plan, domain locking and some Domain Control Panel features will be unavailable.