Question: Can you install a hardware driver, built using WinUSB, along with a C# application deployed using Click-once?

Answer: 
ClickOnce cannot install a driver.

ClickOnce simply copies files from a server location to a client's profile and keeps them in sync. The main reason people get confused is because Visual Studio does extra stuff when you use it to deploy. It creates both a web page and a bootstrapper for prerequisites. The bootstrapper bundles all your prerequisites into a single package but is totally separate from ClickOnce.

You could include your driver in the bootstrapper, but users are ultimately responsible for deciding whether or not to run the bootstrapper before your ClickOnce app. Another option would be to use ClickOnce to deploy the driver file and then write custom code in your application to install it. This assumes your application is able to start without the driver installed and that the user has enough privilege to install the driver.

If you come up with a working solution, please follow up.
Drivers can be uninstalled. My ClickOnce apps deploy the driver files locally on install, then my app checks to see if the USB device is present and if the drivers have been applied. I think this is best, because the user gets the correct error for their situation. If the drivers aren't there, I prompt the user and runas or simply run the installer.