Usually, I can play even if Origin isn't connecting (or if my internet connection is down). Yesterday was a problem because you had to sign in to Origin in order to get to the game, and that wasn't working. I don't usually have to sign in - I always check 'stay signed in' when I do.
Generally, I understand the need to protect the game from piracy, as long as it's not too intrusive. And I actually do find Origin to be a convenience in terms of buying DLC and installing it. I was not a happy camper yesterday, though, at least until I was finally able to get into my game.