There doesn't seem to be any documented way of using this function here, and I'm sore most people trying this are going to default to using a busy loop if there is nothing else to do while waiting (in which case pg_get_result would be better, since it just blocks until a result is ready) or a sleep loop if trying to cancel the query after a certain time.

The C documentation for libPq reccomends using PQisBusy (the C equivalent of pg_connection_busy) by waiting on a socket instead, which lets you timeout if the state doesn't change after a certain period but immediately react if it changes. If you want to cancel after a timeout, you would have something like this :

<?php
class SomeKindOfTimeoutException extends Exception { }

class SomeKindOfSQLErrorException extends Exception { }

function query_with_timeout($conn, $query, $timeout_seconds) {
    assert(pg_get_result($conn) === false); // Ensure that nothing is running

    $socket = [pg_socket($conn)];
    $null = [];

    $dispatch_ok = pg_send_query($conn, $query);

    $still_running = pg_connection_busy($conn);

    while($still_running) {
        // https://www.postgresql.org/docs/current/libpq-async.html
        // "A typical application using these functions will have a main loop that uses select() or poll() to wait for all the conditions that it must respond to."
        // "One of the conditions will be input available from the server, which in terms of select() means readable data on the file descriptor identified by PQsocket."
        // PQisBusy is mapped to pg_connection_busy
        stream_select($socket, $null, $null, $timeout_seconds); // Will wait on that socket until that happens or the timeout is reached
        $still_running = pg_connection_busy($conn); // False on timeout, true if complete

        // You could keep polling like that, this just breaks and throws immediately on first loop
        if ($still_running) {
            $cancel_ok = pg_cancel_query($conn);
            throw new SomeKindOfTimeoutException("TIMEOUT");
        }
    }

    $res = pg_get_result($conn);

    try {
        $error_msg = pg_result_error($res);
        if ($error_msg) throw new SomeKindOfSQLErrorException($error_msg);

        return pg_fetch_all($res);
    } finally {
        pg_free_result($res);
    }
}

$conn_string = "host=localhost port=5433 dbname=postgres";
$db = pg_connect($conn_string);

query_with_timeout($db, "SELECT pg_sleep(10)", 3); // Will throw
?>

pg_connection_busy() returning true does not necessarily mean that there are results waiting for pg_get_result(); it also stays true for some time after a query that causes any sort of postgres error. (See http://bugs.php.net/bug.php?id=36469)