pg_send_query would not stop your script from executing but it would stop the script from exiting.
Example:
<?php
$con = pg_connect('dbname=payroll');
pg_send_query('SELECT process_payroll()'); // Where process_payroll is a super long process
?>
You would still need to wait for the query to finish before the any display would be sent to the browser. And surprisingly, unlike pg_query this script would not generate the Maximum execution time error.