You do not need a center bracket for the True Latch brace to work.  However, it is a nice to have item.  If you were able to attach a 2x4 in the middle AFTER the gate was pre-lifted and braced with the True Latch, then, that would be the ideal time to attach the 2x4 and the center bracket. Don’t install the middle 2x4 in the saggy, lowest position.  If you do, you will have more friction to overcome from the new 2x4 and pickets freshed fastened in that low, sagged state.