Note that this function only registers a single callback as of php 5.4. The most recent callback set is the one that will be executed, they will not be executed in order like with register_shutdown_function(), just overwritten.
Here is my test:
<?php
$i = $j = 0;
header_register_callback(function() use(&$i){ $i+=2; });
header_register_callback(function() use(&$i){ $i+=3; });
register_shutdown_function(function() use(&$j){ $j+=2; });
register_shutdown_function(function() use(&$j){ $j+=3; });
register_shutdown_function(function() use(&$j){ var_dump($j); });
while(!headers_sent()) { echo "<!-- ... flushing ... -->"; }
var_dump(headers_sent(), $i);
exit;
?>
Results:
headers_sent() - true
$i = 3
$j = 5