Following on from what Lucas was saying, I think it depends. If you have a single page app and the page is loaded before you lose connection, you should still be able to interact with it (based on own testing) because the page has already been served - might need a technical opinion on that.
For data storage, you could utilise local or session storage in the browser to store data and then send it back and clear once connected again. There are caveats though:
1. You'd need to figure a way to detect a lost connection.
2. It'd likely only work with a single page app.
3. Local storage is saved in the browser until the browser data is deleted.
4. Session storage is saved in the browser until the session (tab/window) is closed.
For 3 & 4, ideally your user would not be using a shared machine as this would expose the data and I'd only store non-sensitive data.
The Team toddle team might be able to shed more light on what may be possible in the future or add to/correct anything I've mentioned. Hope that helps! 🙂