Probably yes, although possibly no, since rate of heat transfer depends on flow rate past the heat transfer surface.
Given that the AP1000 manages for 72 hours solely with "hot water rises, cold water sinks" levels of flow, a submerged reactor could probably remain cooled indefinitely, although salt water corrosion would then become a part of your life.
Given that the AP1000 manages for 72 hours solely with "hot water rises, cold water sinks" levels of flow, a submerged reactor could probably remain cooled indefinitely, although salt water corrosion would then become a part of your life.