How to use a different database to list and manage comments in the backend

You can filter query. See wpdb::query() in wp-includes/wp-db.php.

You get the complete SQL string as parameter. Then look for queries to the comments table:

add_filter( 'query', function( $query ) 
{
    global $wpdb;

    if ( FALSE === stripos( $query, "FROM $wpdb->comments" )
        return $query;

    // Now change the SQL
});

But you have to catch all the JOINs with other tables too. Not sure if this is possible in an elegant way.