Yes, but not all the functions are available in the 'offline mode'.
You can do all the common things like add food from Favorites, Recents and categories, track water, track weight and measurements and change your Settings.
In order to get data synced to other devices after the changes you need to have an online connection again.
However, without an Internet connection you cannot reach our server and because of that, you cannot search for food in the online database or find a barcode, connect to partners, or sync saved data between different devices. The reason why the food data base is not locally stored on the phone and thus also reachable offline is that it is too much data and the amount of data would slow down your phone.