If prices go up enough, more people in San Francisco will decide to sell, same as anywhere else. That itself doesn't increase the actual number of houses in San Francisco, but it does increase the number available to buy in the market, exactly as supply and demand would predict.

Barring physical constraints and local laws, that would also likely spur more building to increase actual units. That isn't likely to happen to any large degree because there are physical constraints and laws, and that's probably what you were thinking of.