I don't have many games in EA app but all of those seem to have shared online and offline profiles. I think it depends on the game because Space Engineers on Steam also has separate profiles for online and offline play. So if I want to continue my online game offline I have to copy save files from game's online profile folder to offline profile and vice versa.
But it seems that all games need to be started in online mode at least once before they work in offline mode when network is disconnected. I assume games require online authentication data stored for offline mode if they haven't been played online with the latest version of EA app.