Chemists: What would happen if someone dumped...?

Calcium carbonate is insoluble and not particularly reactive. It would slowly sink to the bottom of the ocean and then would sit there, not doing much of anything. If there were enough acidity in the ocean to react with it, it would turn into calcium ions and carbon dioxide. Either of these might screw up the ecosystem, but wouldn't do much about the oil leak.

This is a great idea not only would you have tons of oil in the water but another halfassed attempt to clean up the spill by dumping large amounts of an inorganic salt in a small location without foreseable consequences or unknown data about the reactivity of the animals in the water