I found something interesting when I first got the ICON.... I did not have a SIM card in it and I tried to setup the phone (I had a MicroSIM, not a NANOsim) in advance but, It would not let me log into my live account over Wi-Fi for some reason, it kept saying "try again later". I hard reset the phone and tried again, same problem. As soon as I put in a SIM card, it worked fine....
I'm not sure what happened. I just pulled my SIM out and tested all of the items that should work over WiFi and they did. I surfed the internet, sent an email and went into OneDrive. After pulling out my SIM I powered up and I got an error from back up assistant (VZW back up app), and the first time I did an email check I got a connection error and was told try again later. I tried again about a minute or so later and had no issues.
Here are a couple of questions. Which type of WiFi network were you connected to? Your home network, or a public or some other WiFi hotspot? If the later, it is entirely possible the network connection wasn't that great and couldn't get all the way through and since the SIM was out, was unable to connect via LTE.
After putting the SIM back in, did you activate the phone first BEFORE logging into your Live account? Or did you log in to your Live account, THEN activate the phone? If the later on this, then it DOES work as WiFi only, because the SIM is not activated and the phone is not accessing the internet via LTE.
Does that make sense?