Just add

zend_extension="/usr/local/php/modules/xdebug.so"
xdebug.profiler_enable_trigger = on

to php.ini and then add this line to drupal_web_test_case curlExec just after the second line, where $url is assigned: $curl_options[CURLOPT_URL] = $url . (strpos($url, '?') === FALSE ? '?' : '&') . 'XDEBUG_PROFILE=1'; is the trigger for the profiler.