Although this deconstruction by the Naked Watchmaker seems to suggest otherwise based on the exploded view CAD drawing. www.thenakedwatchmaker.com
7
That said it could have been omitted there and there isn't a physical disassembly of the balance shown. I might write to Breguet just to satisfy my curiosity. Either way though the parachute is at the very least a fine example of craftsmanship.