This offset is only used when drawing things, and no, it's not inefficient at all - the image drawing itself takes a lot more time than two simple additions anyway. It surely is easier to work with than actually moving all game objects whenever your player moves, because that's mixing up the situation with it's visual representation. For example, how are you going to tell that an object hasn't moved? If objects are moved because they need to be drawn somewhere else, things like that become difficult to tell.

You should offset everything, including the player (except for overlay images, such as a heads-up display). To keep the camera centered on the player, just move it whenever the player moves. Whenever you want the camera to focus on something else, you set it's position to that objects position. Every object stays at the same location, they're just rendered somewhere else.