Yes and no. There are essentially two modes of AirPlay, local and streaming.
Local AirPlay (or peer-to-peer) does not require wifi or an internet connection. This is used when mirroring your iPhone or iPad, such as when showing photos/videos you've recorded, or when playing a game; or from your Mac to use as a secondary display. (You cannot mirror or show video that you have downloaded through Netflix, Disney+, or tv+ to watch offline. They are only viewable on the device itself.)
Streaming AirPlay requires a wifi/internet connection and behaves much like the Chromecast. Your phone basically hands it off to the Apple TV and tells it to start downloading this Disney+ video and play it. After this, the phone is completely out of the picture. It could even be turned off and the content will still be playing on the TV since it's going through the internet and not the phone.
Now, depending on your data plan, you could just connect the Apple TV to your hotspot and stream directly from there. Don't worry about using AirPlay. If this is something you're able to do, another option would be to get a cheap Roku. They have all the popular streaming apps, including tv+ (and even support AirPlay). A Roku would also use less data than an Apple TV.
