No, you are getting the two systems confused.
Some of the exhaust fittings are metered fittings for controlling the water flow. In no way shape or form does the exhaust or any cooling lines connect to the battery or the intake silencer or air vent system.
I was saying the white plastic 90 degree elbow in the very first post installed on the black plastic fresh air baffle might have a check valve in it to prevent water from coming into the battery. In my experience though seadoo just put the outlet in a pretty splash proof location so it is just an open vent for the battery..