Depending on the MySQL server setup the SSL certs used may not be in the trusted store, if that’s the case mysqli_ssl_set() needs to be called to set custom keys and certs before connect. This Plugin adds a custom DB class that allows these settings to be configured via custom constants.
This plugin will also add a custom item on the «At a Glance» section of the Dashboard to show if the $wpdb connection is secure or not.
Also find me on GitHub.