Yes, the wire going to the BATT pin needs to be live at all times. This helps the ecu retain its memory, all of what it has learned while running after the battery was connected. In case its not live at all times and only gets 12v when the ignition is turned on, each time you turn the car off, the memory will be cleared and it'll start the learning process again each time you start the car. Which means that it will never have the ideal fuel mixture, idle speed, etc.
The +B and +B2 however need to get 12v through a relay which is energized when the ignition switch is turned on. Again, emphasis on both being fused.