Not exactly. A lot of the carbon is incorporated into the bodies of microbes and fungus that participate in the decomposition process and remains sequestered in the soil.

Ruminants are an important component of the natural carbon cycle, too, farts and all. The buffalo collaborated with prairie grasses and regular wildfires over many thousands of years to build those deep soils that the European settlers found when they arrived in the Great Plains.

What makes good soil black? Carbon. Where does the carbon come from? CO2 metabolized by photosynthesis and incorporated into plant roots, stems, and leaves. @koby is correct.