Academia has come up with several scenarios like this. A friend of mine at MIT told me about a similar idea in which they considered using iron filings to promote plankton growth. The problem with solutions like these is that they are likely to introduce their own problems. Case in point: I'm no chemist, but wouldn't adding a large enough amount of lime to do this have a pretty major effect on the pH?
Yes. A few degrees of temperature fluctuation are already having a significant impact on marine ecosystems (coral reefs). Making all of the world's ocean water more alkaline is pure insanity. It is extremely likely to cause mass extinctions of organisms which evolved to live at a specific water pH level. These extinctions will reverberate through the entire food chain, all the way up through commercial fisheries.
Ecosystems are complicated, and no one fully grasps all the variables. Climate change needs to be addressed, of course, but drastic interventions are likely to have drastic and unforeseen consequences.
