My understanding is live translations do not require an active Internet connection.
> Live Translation is integrated into Messages, FaceTime, and Phone to help users communicate across languages, translating text and audio on the fly.1 Live Translation is enabled by Apple-built models that run entirely on device, so users’ personal conversations stay personal.
https://www.apple.com/newsroom/2025/06/apple-elevates-the-ip...
If it works, that is really impressive. I’m looking forward to trying it out. I’ve always wanted a real-life babelfish for eavesdropping on conversations in foreign language :)