How has earth's atmosphere been influenced by the fact that, as part of the carbon cycle, some amount of organic carbon is stored in sedimentary rocks and is not immediately re-introduced back into the atmosphere?

Organic carbon in the form of coal deposits and also as forming from the small marine organisms hard shell calcium carbonate has helped to remove carbon from the atmosphere. The calcium carbonate formation or many limestones formed especially commonly in the Palaeozoic era in warm shallow seas and sea margins. The carboniferous period between the Devonian and Permian periods was a period when much of the world''s coal was formed. The removal of carbon and carbon dioxide from the atmosphere, would most likely result in a cooling trend and that may explain why the Permian had significant glaciations such as occurred on Gondwana before it broke up (there is evidence of this glaciation in South Africa).. 

Answeris associated with sunny,dry weather;

Answeroil-shale;