John Martin suggested seeding the South Pacific with iron ("The Iron Hypothesis") to increase the photosynthetic activity there. (Here's a clip of Richard Barber describing the idea.) If this increase is to sequester CO2, some of the carbon fixed from the atmosphere has to fall into the deep ocean rather than being respired by animals. Generally, live animals don't fall into the deep ocean, but excrement (referred to as "marine snow") does. So far as I know, nobody knows the carbon content or overall rate of this marine snow, and certainly nobody has any idea how it might change if you dumped a bunch of iron into the water.
One thing is clear though: dump iron into any of a number of spots in the ocean and you get a massive increase in biological activity. More phytoplankton, more zooplankton, and according to one report, more larger fish from surrounding areas swarming in to eat the bounty. This makes sense to me: these productivity spikes have probably been happening for millions of years from dust storms. Fish can probably smell the extra nutrients or some other related effect, and I'm sure the effect is like a temporary oasis in a desert.
What is less clear, but certainly possible, is that the increase in productivity at the base of the food chain leads to an increase farther up. That's interesting to me because I don't eat a lot of zooplankton myself, but I do enjoy tuna, salmon, and a number of other pelagic fish which are all under pressure from commercial fishing. I'd certainly support my tax dollars going to a study to find if iron seeding increased the productivity of a fishery. If it did, you'd think the commercial fishermen would be more than willing to take some iron fertilizer out with them on each trip.
Fishery fertilization might significantly improve the global human food supply, both in quantity and quality. If it works, you'd have fairly wide-scale and sustained fertilization, which would make the carbon sequestration (and other) effects of fertilization much easier to study. After a decade or two of that, you might have enough information to know whether more massive fertilization might help with the global warming problem.