The short answer is no. Like those sold in box stores, a standalone router requires a modem or ONT as it does not read Internet signals on its own. Cable and DSL internet send data across copper wires. Fiber internet transmits signals using light passed through glass fibers. All three connections require a device to translate the signals into data that the router can use and deliver to your devices.
The actual process of routing signals is where a router gets its name. The good news is that if you buy a router, almost all modems output the translated Internet signal through an Ethernet cable. So you can easily add a router to your network to enable routing via more Ethernet cables or Wi-Fi.
If you have cable or DSL internet, you will have a modem to translate an electrical signal. If you have fiber Internet, you will have an ONT to translate the light signal to digital.
If you select WAVE Rural Connect as your service provider, you have the option to add Managed Wireless service, which comes with an advanced hybrid ONT/router.