If you do add or update the watchlists, stock parameters or app colours when you do not have Internet access, these changes will stay local and of course not sync to your other devices. However, the iCloud syncing magic will kick in again once the Internet again becomes available.
For starters this is an app that is designed to need the internet. All stock prices are fetched and updated from our stock supplier via the internet. However, if you already have stocks and prices loaded, you can still analyse the Point and Figure charts without internet data. You can also setup new watchlists and change stock parameters or app colours. However you cannot add new stocks or update the prices for existing ones.