So the documentation on this function is pretty barebones (as is the case for a lot of thin PHP wrappers around C functions), but from what I've gathered by reading the libpq doc and trying various things, you should probably know the following :

* Polling the connection while the underlying socket is busy will cause the connection (or at least the polling, I'm not sure) to fail.
* As stated by the libpq documentation, "do not assume that the socket remains the same across PQconnectPoll calls"
* The socket will become ready after every change in connection status, so the connection must be polled multiple times until the function returns "polling_ok" or "polling_failed".
* "polling_active" can never be returned by libpq and has literally never been used anywhere ever, it has been an unused constant since day 1.

What you need to do is use pg_socket get a PHP stream object corresponding to the current socket and wait after it before polling, like so:

<?php
function pg_wait_connection_ready($conn) {
    assert(is_resource($conn));
    assert(get_resource_type($conn) === "pgsql link" || get_resource_type($conn) === "pgsql link persistent");

    // "On the first iteration, i.e. if you have yet to call PQconnectPoll, behave as if it last returned PGRES_POLLING_WRITING."
    $poll_outcome = PGSQL_POLLING_WRITING;

    while (true) {
        $socket = [pg_socket($conn)]; // "Caution: do not assume that the socket remains the same across PQconnectPoll calls."
        $null = [];

        if ($poll_outcome === PGSQL_POLLING_READING) {
            stream_select($socket, $null, $null, 5);
            $poll_outcome = pg_connect_poll($conn);
        } else if ($poll_outcome === PGSQL_POLLING_WRITING) {
            stream_select($null, $socket, $null, 5);
            $poll_outcome = pg_connect_poll($conn);
        } else {
            break;
        }
    }
}

$db = pg_connect($conn_string, PGSQL_CONNECT_ASYNC);
// Do things while the connection is getting ready
pg_wait_connection_ready($db);
pg_query($sql);
?>