Yes, Disney+ supports Apple TV HD (4th gen or later) and Apple V 4K running tvOS 11.0 and later.
Some tips to remember:
Unfortunately, Disney+ does not support 1st, 2nd, and 3rd-generation Apple TV devices.
To enjoy the best stories in the world on your Apple mobile device, we recommend using a high-speed Internet connection and the most up-to-date mobile and app software. See how to test your Internet connection.