Using $wpdb Class to Pull Recent Comments Across a Network

Why not use get_comments(), instead of trying to roll your own with $wpdb?

function display_sitewide_comments() {
    $sites = wp_get_sites();
    $network_comments = array();
    $max = 20;
    foreach( $sites as $site ) {
        switch_to_blog( $site->blog_id );    
        $args = array(
        'number' => $max,
            'status' => 'approved',
    );
        $network_comments[$site->blog_id] = get_comments( $args );
        restore_current_blog();
    }
    // inspect the comments
    var_dump( $network_comments );
}

Edited to add:

If you just want the 20 most recent comments, you could change $network_comments[$site->blog_id] = get_comments( $args ); to something like

$comments = get_comments( $args );
foreach( $comments as $comments ) {
    $network_comments[] = $comment;
}

Then, at the end of the loop, use usort() to sort the comments based on $comment->comment_date_gmt and then truncate it to $max values.

References

• wp_get_sites()
• switch_to_blog() & restore_current_blog()
• get_comments()