Do my appointments automatically sync while the Notes App is offline?

Appointments are synced only when the Smart Pen is connected to the Moleskine Notes App via Bluetooth.

If you write an event off-line (you write in Smart Diary/Planner PRO with your Smart Pen turned on, but without connecting to the Notes App) the event/s in question will be synced to your calendar the moment you connect your Smart Pen to the Moleskine Notes App.