Is Tornado really non-blocking?

Tornado advertises itself as "a relatively simple, non-blocking web server framework" and was designed to solve the C10k problem. However, looking at their database wrapper, which wraps MySQLdb, I came across the following piece of code:

def _execute(self, cursor, query, parameters):
    try:
        return cursor.execute(query, parameters)
    except OperationalError:
        logging.error("Error connecting to MySQL on %s", self.host)
        self.close()
        raise

As far as I know calls to the MySQLdb, which is built on top of libmysqlclient, are blocking.

Am I right in thinking that a long-running query would render the entire Tornado server unresponsive until it finishes or is there magic on the code?