I believe that all functions seem to work on wifi provided there is an established Bluetooth connection with the phone first. I ran a few tests  on wifi
1- shut off BT on phone- watch working all functions go (Edit- see below no calls)
2- shut off wifi on phone- watch lost connection, red disconnect icon displayed. No functions 
3- next turned wifi on phone. No change in watch, no connection
4- restarted watch, phone still on wifi only. No connection after watch restarted 
5- turned on BT on phone wifi still on. Immediate connection on watch. All functions
6-  turned off BT on phone. Watch still connected via wifi
Simply seems like the watch needs a BT handoff in order to exchange network information so it can stay connected on wifi. 
That's my science project for Saturday morning. Any input from my geek brethren ?
SS 42 model