<?php
/** Repository */
$query = $this->createQuery();
$sqlParts = $this->queryParser->parseQuery($query);
$query->statement($sqlParts, array());
return $query->execute();
?>

Execute at some points end up being in the core function:

<?php
/**
 * Returns the object data using a custom statement
 *
 * @param Statement $statement
 * @return array
 */
protected function getObjectDataByRawQuery(Statement $statement) {
    $realStatement = $statement->getStatement();
    $parameters = $statement->getBoundVariables();

    if ($realStatement instanceof \TYPO3\CMS\Core\Database\PreparedStatement) {
        $realStatement->execute($parameters);
        $rows = $realStatement->fetchAll();

        $realStatement->free();
    } else {
        /**
    This is the part where the query is executed. The only problem is, that $realStatement->getStatement() returns an array.
This is then used to call $this->databaseHandle->sql_query, which expects a SQL string.
Obviously the $result is gonna be NULL, as sql_query cannot handle the given array.
In the end the core will fail at the following function:

Fatal error: Call to a member function fetch_assoc() on a non-object in /~/typo3_src/typo3/sysext/core/Classes/Database/DatabaseConnection.php on line 1044
        */

        /**
         * @deprecated since 6.2, this block will be removed in two versions
         * the deprecation log is in Qom\Statement
         */
        if (!empty($parameters)) {
            $this->replacePlaceholders($realStatement, $parameters);
        }

        $result = $this->databaseHandle->sql_query($realStatement);

        $this->checkSqlErrors();

        $rows = array();
        while ($row = $this->databaseHandle->sql_fetch_assoc($result)) {
            if (is_array($row)) {
                $rows[] = $row;
            }
        }
        $this->databaseHandle->sql_free_result($result);
    }

    return $rows;
}
?>