Here is the absorption coefficient vs wavelength for water. The green curve is water, the red curve is ice. The higher the value of the coefficient, the more rapidly the energy is absorbed during transmission. The Earth's IR radiation (that magical backradiation) covers 5-70 microns with a peak at about 12. It's not the best alignment in the world, but I guarantee you that with, on average, 12,000 feet of depth to do it with, IR WILL get absorbed by the ocean.
File Water infrared absorption coefficient large.gif - Wikipedia the free encyclopedia
File Water infrared absorption coefficient large.gif - Wikipedia the free encyclopedia