Yes, at least I switch around SIM cards without an issue afterwards. I have 4 cell boards and 2 cell phones. Note you may need a "SIM card adapter" like below depending on the size of your phone SIM card, I bought a set of these and they come in handy when using a SIM card from my phone in one of my cell boards.
https://www.amazon.com/dp/B00YFPDAI0
If you do manage to connect, could you post back? I'm very curious to know what 2G availability there is, since I can only connect with 2G/EDGE mode.
Head to a corporate Verizon store (as suggested elsewhere), get a new SIM from them for free, have them activate it on your new phone.
If that doesn't work:
Get a SIM Adapter Tool, get a new Verizon nano-SIM from above, activate it on your Note 4 using the microSIM adapter, then put it in your Note 8 and profit
I've used a Verizon Note 4 and unlocked Note 8 (currently a Canadian Note 8 with US Unlocked firmware) on Verizon, using method #2, and still using the same number.
If you can purchase through US based Amazon, this might work for you: