That is indeed not possible directly for any model Apple TV.
In a roundabout way, it is possible to use your own travel router in between your devices and the captive network. Then the travel router takes the captive portal part, and your devices connect to your own travel router in a non-captive way. As the name suggests, quite convenient for travelers and other users that want to connect to various networks.
Alternatively, it is also possible to enter the portal credentials semi-permanently through a device profile, as configured through the Configurator Mac app. More suitable for corporate or educational institution settings, due to the semi-permanent nature (no on-device interface for it).