I spoke with Tech Support for help setting up voice mail. I was disappointed to find that "classic" voicemail was not delivering "message waiting" notification until the previously-Verizon Galaxy S7 phone rebooted. If preloaded Visual Voice Mail didn't work, it would not possible to have VVM without a third-party service. If it did work, then Mobile Data would be needed. Verizon's VVM app did not work.
For giggles I installed the T-Mobile VVM app, which didn't work. Some days later I received an SMS message from phone number 128: Visual Voicemail Alert: A new version of My Visual Voicemail app is now available. To access your voicemail messages, you will need to download the latest version of the app. Download now: t-mo.co/VMMmvno.
I installed and not only does it work, it provides prompt notification, and it works without Mobile Data enabled on the phone!