Ok, I just tried again. Turned off WiFi and put phone into Airplane Mode. Verified that Bluetooth is still connected to the watch. Go into the Connect app.

Ok, I just tried again. Turned off WiFi and put phone into Airplane Mode. Verified that Bluetooth is still connected to the watch. Go into the Connect app. There's a big red box that says "No Internet Connection." Heart Rate is transmitting to the Connect App in real time. However, if I try to run a Sync from Connect, it hangs and then fails. Turn on WiFi and take phone out of Airplane Mode. Run a Sync from Connect. It completes successfully. Confirmed - If you complete an Activity and want to sync your watch to your phone with the Connect app, your phone must have an Internet connection.