Can I get Wi-Fi without Internet?

Yes. Since Wi-Fi is actually the local connection in your home, you can have a Wi-Fi signal for the devices in your home to connect locally to each other. This would allow them to share files/documents around the home , on the same network. (IE. A wireless printer would be on your local Wi-Fi connection and you could send your documents internally to it without using the Internet).

The important thing to note is that without an Internet Service Provider (ISP) like Nexicom behind the Wi-Fi signal, you will not be able to access external locations, such as Google, Facebook, Netflix etc.