There must be some quantity of salt we can dump a year to raise salinity. We should be rigorous, and find out what that quantity is. If we can change a climate, we can change an ocean.
Yes, we probably can re-salinate a flow to attempt to alter its dynamics. We'd also have altered its salinity profile in ways which have repercussions on e.g. cod fisheries, or krill, or other things. Thats the problem with complex biological systems with lots of interrelated parts: they don't reverse with simple tweaks because once you change one part, you change lots of parts in unexpected ways.
(I did once study this stuff back in the 80s and was very bad at it, but what I recall of even two-actor predator-prey relationships is that they are remarkably complex, cyclical, and do not just return to the same stable place if you alter them trivially. I believe this is probably even more true for physical systems like weather and climate)
So, to raise salinity by .01%, we'd need 1268 years of normal production (plus some when you exclude sea-water extraction).
[0] http://www.wolframalpha.com/input/?i=(volume+of+the+world%27...
[1] http://www.wolframalpha.com/input/?i=31956+cubic+miles+of+sa...
[2] http://www.saltinstitute.org/salt-101/production-industry/