Ahh damn. Does signing in on the phone first not work? I'm struggling to remember what the captive screen wanted last time I did it, it's been a while.
No. It doesn’t. That’s where the travel router came in. It presents itself as one MAC address using one of its radios and exposes another interface for your devices. I was staying in an extended stay and we had computers and a WiFi printer set up. We were waiting for our house to be built.
I was just informed that Apple added support for captive networks in March.
Then you have to use your data plan. At least with the previous AppleTV, you could AirPlay directly from your iPhone to your AppleTV without the AppleTV being connected to an external Wifi network.
It didn’t work with all iPhone apps though. For instance it didn’t work with Netflix.