How does the communication between Smartwatch and Smartphone work over the same Wifi?
With GPS and offline music support, you can already leave your phone
  at home, then go jogging and jamming like normal. Now Android Wear
  supports watches with built-in Wi-Fi. As long as your watch is
  connected to a Wi-Fi network, and your phone has a data connection
  (wherever it is), you’ll be able to get notifications, send messages,
  and use all your favorite apps. And if you really do forget your
  phone, you can always ask your watch where it is.


From this link.
I hope this text answers your question.