If it is anything like the console version, a surprising amount of character data is actually local. The game can be played entirely offline even. I am testing it right now to see what all you have access to. You have access to all features except the event quests, multiplayer (obviously), arena challenges (though you can still do the regular arena), and the Kulve Siege, which is technically an "event". Everything else is working just fine without connecting online at all. If nothing else, the trainer can be run like the one for SAO:FB where you put steam into offline mode to play the game and use the trainer.