Even if this could be done in a manner that keeps the air safe to continue breathing, the other problem from doing too much of this is that it could increase the Earth's albedo and have a global cooling effect (akin to when volcanic eruptions on earth have caused famines, skipped summers/growing seasons). But in some ways, that may make this the perfect worst-case-scenario solution to runaway global warming. We could periodically use "clean" nuclear detonations to put enough particulates in the air to reduce the global temperature and sequester carbon. Once the particulates settle, if there is still too much CO2, we could do another round of detonations, etc.