For starters it would be helpful if you tell us where is your Note3 from: some countries have no region lock, like China and if you're from one of those places, no worry. If you do have region lock, after using the phone on local network for some time region lock is removed per Samsung. However there were some stories posted around that it wasn't and also it is not clear to me what happens if let's say you do factory reset for some reason. I rooted my phone without tripping Knox flag and then run Chainfire region unlock program to clear all these nonsense and I can confirm the region lock list on my phone was erased and I expect my phone to work as it should on any GSM network.
You need to read around to see if doing something similar is a good option for you.
In theory it should work the way Samsung says.