Swiss balls are fun for BJJ-related exercises, though how good the skills transference is is debatable. Jeff Glover does some crazy stuff on it. I spent a fun filled few hours trying to emulate him, but the ball popped on me and I ended up suddenly sitting on the floor on a sheet of deflated plastic with some training buds laughing at me.
Better for keeping COG centred over imaginary opponent, though once again how well it translates into real BJJ is debatable.
Jeff Glover is a good fighter with a proven contest rep atinternational level, so I'm doing what good fighters do and advocate. No need for the self appointed forum police to attack me.
Standing on the ball might help with balance, but not with "rooting" IMO. A chi sao contest on a pair of Swiss balls would be a pretty short one