There are a few red flags.
Sea water has a lot more in it than water and dissolved carbon mostly in the form of bicarbonates. Sea water is full of life, salts and minerals and those things cling to everything they touch. That's why ship defouling is such a problem.
Fouling of such a plant is a big concern. Desalination plants obviously manage this, but they are working to remove everything except water, not a tiny percentage of specific molecules.
The extra things are often bigger than CO2 molecules as well, making the filters challenging. CO2 can sit in dissolved suspension without bubbling to the surface immediately. That is certainly viable in a simple brine with carbonate ions, but more difficult in real sea water with highly variable constituents.
Desalination makes economic sense where 2.5x the cost of water is required because 95% of what passes through the system is the product, fresh water.
But in this case, the carbon content of the ocean is lower than the carbon content of atmosphere, under 300 ppm or 0.03%.
That means they will have to pump about 3,333 tons of seawater i.e. 3,333 cubic meters to get a ton of CO2.
Then there's the problem of diffusion. Water moves and things diffuse in it, but much more slowly than in air. They are removing bicarbonates locally. That means that the are lowering the ppm locally and getting diminishing returns. There will be some optimal point, but it's going to be likely below 200 ppm, so call it 5,000 cubic meters of water to get a ton of CO2.
Further, one of the big problems of ocean acidification is the shift of carbon atoms into forms inaccessible to shellfish, so they can't form their shells. Excess CO2 uptake does that as noted above, but so does the Captura process. Clearly environmental assessments are going to be concerned about elimination of shell fish mineral requirements. Got a dead ocean somewhere without shellfish?
Finally, there's the big question of what we are going to do with the CO2. Sequestration sites aren't magically beside sites that happen to have very low shellfish concentrations and good renewable connections. CO2 pipelines have their own problems.
