should visual voicemail work when on wifi with no cel service?

I have struggled now for two years to get reliable voicemail delivery on my iPhone SE. I live in an area with no cel service, and used to have a network extender which enabled me to connect to the Verizon network. For some reason that stopped working, and after many attempts and countless hours of tech support, I had to give up on that solution. I have tried new extender devices, a new phone and a different ISP. So, I really need WiFi calling to work as it's my only option. The "calling" part works, but voicemail does not. I will generally get a notification of a missed call, and once in a while a notification that I have a new voice message, but no voicemail messages ever show up on the phone. Often when I return to an area with service, the missing voicemails appear, but not always.

I recently phrased my search query differently when looking on line for answers and came across some statements that visual voicemail will not work unless the phone has access to the carrier network (Verizon), and that it therefore can not work on WiFi in an area with no cel service. Is this true?

If so it would explain my problem, but I am wondering why on earth Verizon does not know this and why they keep assuring me my phone should work exactly the same on WiFi calling as it does when on the Verizon network. I have talked to A LOT of Verizon people at this point, and not one of them has told me this; instead they tell me my phone should be 100% functional on WiFi calling and should work exactly the same way it does when connected to the Verizon network.