The short answer is: No. Definitely not. But it could theoretically be possible.
Ecologists understand that iron is a limiting resource for big swaths of the world’s oceans. Availability of iron controls primary productivity—that is, how much plankton grow in oceans, and therefore, how much carbon they take in from the atmosphere through photosynthesis.
In a 2004 study published in Science, researchers dumped about a ton of iron into the Antarctic Ocean. They estimated that their efforts created a 1000-square-kilometer plankton bloom which, in the end, transferred about 900 tons of carbon to deep ocean, where it will stay for hundreds of years. That’s enough to offset the effects of about 700 Americans’ yearly emissions from driving, and we could perhaps do way better. Another study found that when sections of ocean are fertilized by naturally occurring iron deposits, the sequestration rate is at least ten times higher.
We are far from even beginning to know what the side effects would be of dumping massive amounts of iron into the ocean. It is sure to be highly disruptive to existing ecosystems. We also don’t know how much it would cost, and whether the impact would scale in the way we expect.
We have climate solutions that we already know to be feasible and effective (solar panels! fewer cars! less meat!), so it probably doesn’t make sense to start recklessly altering major earth systems. But since those reasonable solutions seem to be off the table politically, it is possible to picture a world in which we have to start trying some of these unreasonable ones.