Yes. You can do this:
ignore_user_abort(true);//not required
set_time_limit(0);
ob_start();
// do initial processing here
echo $response; // send the response
header('Connection: close');
header('Content-Length: '.ob_get_length());
ob_end_flush();
@ob_flush();
flush();
fastcgi_finish_request();//required for PHP-FPM (PHP > 5.3.3)
// now the request is sent to the browser, but the script is still running
// so, you can continue...
die(); //a must especially if set_time_limit=0 is used and the task ends