FedUp33, Visual voicemail content and their notifications populate when cellular data is engaged. That is confirmed by Apple and is not carrier specific (although some carriers can block visual voicemail based on your data plan.
You can view visual voicemail but you may not be able to download new visual voicemail while on WiFi. You also may not receive notifications for the voicemail messages while on WiFi.
FedUp33, if you are using iMessage, you can send the MMS over wifi.
We do have wiFi calling. it went live for iPhones a few weeks ago. You can get more details about that here: