Wordpress - Does a query executed through wpdb class get cached?

Nope, doesn't work like that. The database-related caching is minimal and mostly covers using precisely same queries during single page load.

Best way to cache persistently database and/or computationally intensive results is using Transients API to store results for fitting period of time.

The docs suggested that the output from a query was only cached for that specific request - so presumably WordPress is doing a buffered query on MySQL.

In my case, I used the wp_cache_* functions - see http://codex.wordpress.org/Class_Reference/WP_Object_Cache

Example code:

sql = "
    SELECT {$wpdb->posts}.* FROM {$wpdb->posts}
    LEFT JOIN {$wpdb->term_relationships} ON ({$wpdb->posts}.ID = {$wpdb->term_relationships}.object_id)
    LEFT JOIN {$wpdb->term_taxonomy} ON ({$wpdb->term_relationships}.term_taxonomy_id = {$wpdb->term_taxonomy}.term_taxonomy_id)
    WHERE ({$wpdb->term_taxonomy}.taxonomy = 'category' AND {$wpdb->term_taxonomy}.term_id = 9849 )
    AND
    {$wpdb->posts}.post_status = 'publish' AND
    {$wpdb->posts}.post_type = 'post' ORDER BY {$wpdb->posts}.post_title ASC";

$posts = wp_cache_get(md5($sql), 'somerandomkey');
if($posts === false) {
    $posts = $wpdb->get_results($sql, OBJECT);
    wp_cache_add(md5($sql), $posts, 'somerandomkey');
}

if(empty($posts)) {
    echo "<p>No results found </p>";
}