Is the ocean a carbon sink when considering only the biospheric component?
Yes, the marine biosphere is a carbon sink, and a very important one. It is known that the oceans produce more oxygen and biologically consume more carbon dioxide than all the tropical rainforests. This is done by microscopic blue-green algae, cyanobacteria and phytoplankton of many kinds. Also by green algae such as seaweeds, by sea grass meadows, and by coral reefs which are built of calcium carbonate synthesised by the corals themselves. Sea grass is an interesting plant, related to land grasses but able to survive and prosper in shallow seas where there is plenty of light and suitable soil. It is very important for the marine ecosphere. As on land, there are marine deserts where there is very little biological activity, and other areas that are teeming with life.

The question arises of how much of this captured carbon remains in the sea. The answer is most of it, but it is impossible to give exact figures. Some of the marine biomass is removed by various means, fishing for example, but that does not mean that all the carbon is returned to the atmosphere. Sea birds consume a lot of fish, and much of their guano is deposited on land, and some of them die on land, but again not all the carbon is returned to the atmosphere. There are enormous deposits of guano on the coast of South America and some Pacific islands, which are mined for fertiliser. The bodies of dead marine creatures, and sometimes live ones, are often consumed by other marine creatures. A dead whale, for example, provides a feast for all sorts of marine carnivores and scavengers. Much of the marine biomass eventually sinks to the ocean floor, where it becomes part of the ooze and sediment.