Offline or not, I'm sure Google uploads every keystroke, phone orientation, photo, WiFi endpoints and your shoe size when you interact with it. To enhance your experience.
At a glance, I see they do gather analytics about how much the app is used (model downloads, model invocations etc) without message content, pretty much just the model used.
The funny thing is that a lot of Google's internal training content uses an imaginary product "gShoe", and discusses the privacy implications of data that such a shoe might collect :D