My Supernote is off or away — can I still get a note I haven't opened before?

Usually, yes. When the app can't reach your device, the note dialog offers two options. Option 1 (recommended): enable Browse & Access on the Supernote — that connects directly to the device and gets your very latest ink. Option 2: sync the note from the Supernote cloud — the app downloads the last copy your device synced there. The cloud copy needs your Supernote's cloud sync to be on, and it may not include your latest handwriting unless the device synced recently. Before downloading, the app checks the cloud and tells you when that copy was last synced, so you can decide.