It seems like anyone who would pay to be a geisha's mate is a jerk. Dr. Crab. Nobu. The Chairman. And the Baron. None of these are good examples of how to be a gentleman.
The Baron is Mameha's danna. He looks like some kind of tree nut "because he was small and very round" (15.92). And not that a geisha expects fidelity, but the Baron tries to get with Sayuri. He thinks he can have Mameha and undress her apprentice, too.
The Baron serves as a bit of a foil to the Chairman. Both men have similar motivations—buying a mistress. But they treat them in different ways. One big difference between the two men is that the Chairman lets Sayuri have his child. The Baron forces Mameha to have three abortions. Sayuri loves the Chairman (or she thinks she does), while Mameha seems to have no feelings for the Baron. She doesn't seem to care at all when he dies.
Moral of the story? Not all danna are created equally.