Steam offline mode will prevent updates yes. You will not, however, be notified by Steam when there is an update. Nor will you receive pop-ups relating to new releases. You may be notified in game of new content, if Gearbox send such notifications.
While offline, you can still earn achievements, but those won't appear in Steam until after you go back online.
Now, while you can tell Steam to not auto update your game from the right click context menus, be aware that doing so does not prevent updates it only delays them until you launch the game.
Going into offline mode is the only way to prevent updates from ever being applied. However, offline mode is only good for a limited amount of time. Once that amount of time has passed, you will be prompted to go back online before you can play again. As for the length of that time? It's undisclosed and may be set differently for different games.