What require_wp_db function in Wordpress would look like, if it worked

require_wp_db_patch.php

<?php
function require_wp_db() {
    global $wpdb;
    if ( isset($wpdb) ){
        return;
    }
    // Should check for override db.php file first
    // - including both means fatal error on duplicate class
    if ( file_exists( WP_CONTENT_DIR . '/db.php' ) ){
        require_once( WP_CONTENT_DIR . '/db.php' );
    }
    // include core default
    else {
        require_once( ABSPATH . WPINC . '/wp-db.php' );
    }
    // The db.php adapter may have defined the global for us
    if( ! isset($wpdb) ){
        $wpdb = new wpdb( DB_USER, DB_PASSWORD, DB_NAME, DB_HOST );
    }
}

This patch isn't necessary. Your db.php file shouldn't define the wpdb class, it should define a class that extends it and then instantiate it (unless you want to write a completely new db driver class from scratch, then you don't need to extend wpdb).

Example db.php:

class my_db_driver extends wpdb {

    public function some_method_i_want_to_override() {
        // Hello!
    }

}

$wpdb = new my_db_driver( DB_USER, DB_PASSWORD, DB_NAME, DB_HOST );

Sorry, got tripped up by the comment editor there.