It is all about particle size of the suspended CaCo3. Nanoparticles can even be produced with ultrasound via CaOH2 + CO2 precipitation which would have much better adsorption characteristics than just CaCO3 dust.
It probably doesn't just bind organic molecules, I'm sure that there is a myriad of effects that play out with other ions in seawater, much too complicated to pin down. Inorganics will likely adsorb to some extent I bet.
I would not be surprised if corals are capable of incorporating consumed CaCO3 particles of a certain size, the bound organic/inorganics would at least get consumed for sure. If a coral captures CaCO3 from the water bound with food why would the coral release it?
I think I read that certain zoas and protopalys incorporate the CaCO3 substrate they are growing on into themselves.