You should be able to answer that for yourself. Just visit https://www.whatismyip.com/ periodically, or any equivalent service if you don’t like that one.
It is impossible to generalize across all VPN service providers but I would say mostly: the IP address is set when you connect to the service (and won’t change unless you disconnect and reconnect).
As @amarok says, the behavior you want depends on your threat model.
As a follow up, I got it to connect on my home network with no issue without disabling anything, but not my work wifi. There is no GUI, so I really have to learn all the commands to changes countries, have it connect automatically all the time, how to disconnect/connect to change IP addresses daily, switching countries, or something, etc. Lots to figure out.
For right now, I’ll just manually connect and not even sure where to look to see if I am connected, other than the terminal after entering nordvpn connnect.
You can set up your various country/server connections in Network Manager. Then it’s just a matter of clicking on the Network Manager icon and choosing the one you want with the mouse/pointer. You’ll have to make and save a separate connection for every server you think you’ll use, but it’s not hard at all.
https://support.nordvpn.com/Connectivity/Linux/1061938702/How-to-connect-to-NordVPN-using-Linux-Network-Manager.htm
I’ve done this before with a different VPN provider who didn’t have a Linux client.
To see if you’re connected, just hover over the Network Manager icon.
If you are using some flavor of Firefox, NordVPN has an extension that will give you a limited GUI access to their command line-based client. I use another service, so I cannot attest to its usefulness, but you may wish to try it.
Mine has something similar. It allows me to pick a location, connect, change some settings–not all–etc. Of course, one needs to start Firefox first. I start Firefox, set up my VPN to connect, and then I access wifi.
PS. Here is that link.
Interesting that NordVPN support did not mention that in my emails with them, but thank you, I will look into that. I only have the included browser with LibreWolf and Brave browsers right now.
Just another curious observation for a newbie like me, but I can connect to the NordVPN at home now, anytime, no issue. But cannot at my work on their wifi. Not a big issue, as it seems to stay connected if I just close the lid and now power down on the way to work. But my curiosity has be wondering.
Were you able to connect at work previously, i.e. with a different computer or OS, and NordVPN?
no, today was the first time I went and disconnected, then attempted to reconnect several times. Like I said, no big deal, but curious.
I did switch the connection protocol to TCP as support suggested, and disabled IPv6 as they suggested. It seems to try to connect, but after several minutes it says connection failed.
I also admit it’s more frustrating me not seeing any GUI saying I am, or am not connected, etc. The "what’s my IP? website is the easiest way to see what my IP is, and if it has changed, and where it is. Oh, well, I’ll look into it more tomorrow.
If you set up your various server connections with Network Manager (or any other Linux network client), you should be able to see at a glance if you’re connected or not.
I’m just not seeing how to do this. When I open the network manager window and click on VPN’s it shows that there are none, and none to add?
Odd. Came in this morning to work and did an OS software update and then tried to connect and it connected OK although it did take about four or five minutes. 
@amarok may have other instructions, but when I did this with my previous service, I downloaded the server configuration ovpn information from my VPN provider which they furnished in a zip file. I imported many into the Network Manager. (As I recall, NM has a limit. It was one of the reasons I changed services; my VPN offered over a hundred servers and many locations, but I could only use the handful I imported within Linux itself. I wanted real Linux support.)
I wish I could offer more, but I have not used NordVPN. I have a friend who does, but he uses Windows and iOS.
I mentioned the browser extension for Firefox that my service has. It does have a little icon, so I can tell at a glance that I am connected. Unfortunately, I am not a Brave user either, so maybe I should be quiet… 
I linked the instructions for NordVPN a few comments back:
Basically, download their .zip, right-click on it, and extract it (unzip it). Extracting it to the Home folder is easiest.
Right-click on the Network Manager icon in the corner of your screen, select Edit Connections, click “+” and then choose “OpenVPN”.
Then follow NordVPN’s guide to fill in the fields, navigate to your Home folder, and choose one of the configuration to add it to the “CA Certificate” field.
Add your NordVPN username and password, then “Save.”
Add as many different configurations (i.e. servers) as you want; you’ll have to repeat the above steps for each one.
To connect to one of your saved configs at any time, left-click on the Network Manager icon and select it with the cursor.
Note that I’m using Linux Mint, so things may look slightly different in your PureOS menus, but it should be similar.
So each file in each folder is a server? One folder is ovpn_tcp, the other is ovpn_udp
I used a file from the udp folder since that is what was in the example 
Yes, that’s correct. Unfortunately, they don’t seem to be labeled in a user-friendly way, in that you can’t tell by looking at the list which server goes to which destination. (Unless the latest download has corrected what I see on their website example.)
UDP vs. TCP
Here’s what AirVPN says about it: https://airvpn.org/faq/software_protocols/
TIP: Name each VPN connection as its location, to make it easy to choose quickly.
It’s a shame NordVPN has no immediate plans for a GUI interface. But I’m sure by next August when this subscription is up, I will have found a replacement VPN to use. And thank you again for all your help!
Just choose your replacement well! See: https://restoreprivacy.com/vpn-review-websites-owned-by-vpns/ and Librem Tunnel and the acquisition of Private Internet Access
I’m just beginning to look into the Rob Braxman VPN, and see what I can learn about how that has been received.
I myself don’t know anything about his VPN service, but I think I would go with a tried-and-true company rather than a one-man operation (if that’s an accurate description…I don’t know).
I do respect his Custom ROM service, though!
I normally subscribe to two different VPN providers, just to have options and back-up.
What VPN’s do you use, if I may ask?