I'm ignoring the climate debate and making this purely about a point of science. The carbon in coal was once part of the atmosphere in one form or another. There is no such thing as "new carbon", just different forms of it.
Burning coal is not in any way, shape or form "introducing new carbon into the environment". It is releasing carbon otherwise sequestered, just like your submerged forest, increasing water temperatures reducing the solubility of CO2 and all the other bit part players helping with the equilibrium of carbon in the atmosphere.

