Depends on the boat/engine/application whether the exhaust is water cooled. Many of the performance boats particularly in the southern states don't, they just run open headers going up and out the back as per pic.
Probably does have a water cooled exhaust system but you wouldn't cool it before the output side of the turbo, any heat taken out of the exhaust before the turbo isn't there to spin the turbo. Water cooled turbos only cool the bearings, the turbo housing is not cooled.
Mike