Yes, the Amabrush also works with braces. The bristles are soft and flexible. Your braces won't get damaged. If you insert the mouthpiece and slightly bite on it to put it in the right position, the bristles may be bent or misplaced by the brackets.
Therefore just like a normal manual or electric toothbrush, additional care for your teeth with braces will still be required. Interdental brushes are best suited for a complete cleaning when wearing braces. Find out more about it here.