Yes. You can do this:

ignore_user_abort(true);
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();

// now the request is sent to the browser, but the script is still running
// so, you can continue...