By my rudimentary estimation (based on numbers from https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/grl... Figure 3) I believe the annual ice melt in the Arctic each year is approximately 10,000 km^3 of ice. Let's assume all of it flows into the Atlantic. Remove 10% of that volume to approximate the liquid volume of the ice, then convert to kilograms of water = 9x10^15 kg. Average ocean salinity is 35g of salt to 1kg of water. That comes out to ~3.15*10^14 (315 trillion) kg of salt. You can pick a percentage that flows into the Atlantic, but it would still require on the order of trillions of kilograms of salt.

And the answer is that if we turned all of our energy to salt production, it wouldn’t even be a drop in the ocean, and our efforts would of course liberate more CO2 and contribute to global warming. Of all the possible ways we could geoengineer (all of them bad ideas frankly) this has to be one of the worst, least effective, most limited, and least likely to succeed.

If we’re going to hasten our demise, we might as well try sulfate aerosols or something with a more global effect. We’d still end up killing ourselves, but at least it wouldn’t be quite so much like trying to get a sailboat to move by blowing on the sails.