It depends on what app/device/version you're referring to.
On the web - you must be on the site as you lose connection and then can continue using it.
On the Windows app, similar as on the web, but the app can hide in the system tray so as long as it's there you'll have access.
The Mac app also will work offline as long as you have it opened and are logged in.
Our plugins will work as the web, that is - you must access them online first and then can lose the connection.
Our mobile apps feature full offline support so you don't need a connection to access them at all (aside from the first initial login and sync).