Can you connect an Apple TV 4 (the latest one) to a WiFi that requires a username and password?

Depends on what you’re asking, if it’s a home wifi , yes. I use a username and password. I have 2 I use off the same router.

That does not work.

Set up your Apple TV - Apple Support

Apple TV needs Personal Internet (e.g. a home network with no more than a password). It doesn't support enterprise, edu, public or subscription networks with sign-in requirements (captive network portals).

If this is intended for semi-permanent use, then you can collaborate with the network administrator about the use of a configuration profile for this device to automatically connect using the credentials.

If this is intended for guest use (e.g. a hotel), then you may be better off using an in-between travel router.

I’m not the one qualified to assist you with the use of the Apple Configurator app, but the tool is intended for deployment of devices. I haven’t read any indication that that is what you want, though.