I recently bought and setup a Galaxy Watch LTE version. I have learned much through trial and error, research and hours on the phone with Tech Support. Here's what I think I know
1) Number sharing is somewhat of a misnomer. It implies that your two devices are actually linked and anything to and from one number is available on both devices. One might think that since they bought the LTE version of the watch and activated it, they can leave their number shared phone at home with a dead battery and still function as normal with the watch as they run errands out in town. This is the case under only certain conditions. The main condition is that your host device (phone) is ON the network. It can be sitting at home, but it has to be ON. The Host Device (phone) is a critical part of the "number share" process as messages to and from your shared number are processed by the Verizon network.
2) Think of "Number Share" with an activated LTE Watch as nothing more then an extended range Tether. Where as with your phone tethered via Bluetooth, you can roam your house or backyard using your watch; with LTE "number share" , you can roam all over town...BUT the host device (phone) phone must be still be ON and On the network.
3) If you are out and about with your "number shared" watch and your phone is home with a dead battery, then "number share" will not be active and your watch will act like a stand alone device using it's true activated Number. The "number shared" feature will not be in play because the Verizon network can't see your phone at home because of the dead battery. I know this is the case in my situation where text messages are concerned. I have not tried voice calls to and from the actual Watch number when my host device smart phone is OFF. You can easily determine your watches true number at My Verizon.
If anybody disagrees, please feel free to chime in. Because I would like to be wrong about what I've written above. I bought the watch thinking I could number share the watch with my phone and literally leave my phone at home and still be online with my watch. I wasn't aware of the little caveat that the phone can be at home but it must be ON. I feel I got duped by Verizon's marketing.
Maybe a knowledgeable Verizon person can correct my theory, I would love to hear from someone who is an actual expert.