Generally no. These baths tend to be a social gathering place.  Now there are two ways to wash.  One is a communal bath and the other is something more like a shower where water is poured over your body to remove the sweat.  These are more private and I am sure there are alcoves that are more private than other places but nothing like individual rooms that are completely closed off.  I would say there are secluded areas but not exactly private.  The Crimson Palace can be rented out for private functions.