The ntp server ip is currently hardcoded in the firmware (you can change it by recompiling the firmware and then uploading it to the microcontroller).
To implement what you need, you can use the EtherCard::browseurl function. The EtherCard library has a few examples to demo this, for example, the webclient example:
https://github.com/jcw/ethercard/blob/master/examples/webClient/webClient.ino
shows how to use browseurl to periodically get a webpage and send the content to serial.