It's worth noting that the definition of organic matter is kind of arbitrary but also has a specific meaning in soil science.

Seeing as how the carbonate is bound to an inorganic cation instead of something organic, I'd say that it is not an organic molecule in this instance. In addition, it clearly exhibits all of the requirements to be called a mineral (solid, crystalline, specific chemical and physical properties, etc).

In soil science, organic matter refers to (a) living biomass, (b) fresh detritus, and (c) decomposed detritus aka humus. All three are readily oxidized by agents like peroxide, dichromate, etc. Carbonate minerals, on the other hand, do not readily oxidize with this exposure. Soil organic matter has drastically different properties than the mineral portion of the soil, which is the reason why the distinction is made. It's the same reason why we have a differentiation between sand and clay or between calcareous and mollic soils.

Besides, the pedogensis of calcareous soils arguably does not include a time as biomass, even though it is produced by biologically processes. Carbonate shells are formed to protect the organism, but to my knowledge there is no biological function of the carbonate in the organism. That is to say, carbonates locked into the matrix of a shell do not serve as a functional group, but instead as a mineral component.

**I should mention that the first (Seeing...) and third (Besides...) paragraphs are quite arguable and are mostly rooted in my basic understandings of chemistry, mineralogy, and soil science. But the second paragraph (In soil science...) is pretty much a textbook explanation.