To be clear, by setting up a router with wi-fi capability, you are creating your own local network. This network will consist of all of the devices you attach to said network.
If your TV has a wireless receiver, then you should have no issue connecting it to this router, assuming you have successfully configured the router’s wireless network (super easy).
Do note that your local network is completely independent of “the internet” though, and unless you pay for internet through an internet service provider (ISP), you will not have access to the internet.
So why might you want to connect your TV to your local network via wi-fi, and not have any internet access? A popular reason to do so is to stream content you are hosting yourself on a local computer or media server. You can google media servers for more info on that fun stuff.
Ciao for now!