Yes, it does fix acid problems.

The calcium carbonate dust is reflective (the aim of the engineering is to reflect sunlight away from the Earth's atmosphere in the first place). However, it doesn't contribute to acid rain or oceans like the sulfate dioxide does (the aerosol that East Asian scrubbers are removing).

The CO2 (a greenhouse gas) amount isn't increased in this engineering effort. It increases because of burning fossil fuels, though. In the East Asian countries, they are producing/using more energy (via burning fossil fuels), but only removing the reflective aerosol; they're still emitting the CO2.

If cost was no object, we'd probably need to use the calcium carbonate immediately (to prevent the sunlight from entering the atmosphere immediately), we'd scrub existing carbon from the atmosphere (CO2), and we'd convert power plants to non-emissive technologies (and also install scrubbers onto existing ones for as long as they're needed).