With splatter around it I would say it's exhaust relief. When the boat is tied up at the dock or on the trailer in a launching position, the normal exhaust outlet is submerge and offers "back pressure" to the engine which impedes starting. The exhaust relief is a hole in the exhaust channel allowing exhaust gasses and cooling water discharges to exit allowing easier starting.
When running it will spatter at low speeds and if the boat is on plane and running at WOT it could be a solid stream of water.
Otherwise could be a water pump tell tale but they are smaller and located where the operator can see them from the helm and the discharge is a solid stream at idle under a few pounds of pressure.....doesn't meet your criteria.
