connection_status and connection_aborted() rely on the function that outputs the data from the buffer.
Since you do not output any data, there is no way to detect that the connection is dead.

In the manual, it says that when user clicks STOP button, the script should be terminated. In fact, the script keeps running. I checked it by verifying the size of /tmp/abc, which keeps increasing. 

I have tried to send output. It seems that IE maintains its own buffer, that any output can't get displayed before I click STOP button

I make another test. With the following script:
<?php
$str = "asdfasdf5687ju9465870u985tg79yh8";
$str1 = str_repeat($str, 1000);
$str2 = $str;
function write()
{
file_put_contents("/tmp/abc", "Final Connection:".connection_status()."\n", FILE_APPEND);
}
register_shutdown_function("write");
while(1)
{
	$count = 100000000;
	while($count > 0)
	{
	$count = $count -1;
		if($count%1000000==0)
		{
			var_dump($str1);
			//var_dump($str2);
			ob_flush();
		}
	}
}
?>

If large mount of output is sent like $str1, I will get ABORT signal and script terminated. But if $str2 is sent, it seems that no ABORT signal and script keeps running to TIMEOUT