Earlier quoted context omitted.
Not without a significant energy expenditure. But most of our energy sources of course produce CO2 and other products.
I guess the Scifi question is can you build a nuclear ship with some apparatus that pulls the CO2 out of the ocean and breaks it into C (stored on ship) and O (released into atmosphere)?
Most large navies run nuclear reactors on board their ships. IIRC, nuclear submarines pull water and use a portion of reactor power to get fresh oxygen.
But I'm also not sure that the reaction is as easy as it sounds. First of all, manufacturing such a ship would likely cause a great deal of greenhouse emissions. Would the ship's benefit offset the pollution it implicitly creates as it is built? How about the pollution generated by its operation? No engine emissions, but when the reactor gets decommissioned it'll have to be buried, likely by diesel-powered equipment and covered in concrete which is manufactured in a dirty process. Tugboats aren't nuclear powered. Re-fuelling apparatuses aren't nuclear-powered. Crew will produce waste, reactor needs to be cooled which introduces unwanted heat to the water, etc etc etc.
Would it even be economically possible to build/operate?
How many ships would be required to make a measurable impact?