Usual salinity and solubility of NaCl
An usual salinity in the world's major oceans is 35 g/kg. The solubility of sodium chloride in water is around 360 g/kg (Sodium Chloride, Solubility in water). Therefore, the solubility is not the limiting factor.
Sea salt consists mainly of sodium chloride (NaCl). Therefore, this approximation should be OK.
Mixing of salt and water
The salt in the sea water 'moves together' with the water. Thus, when warm water flows from the equator to the poles it transports salt to the poles. At the poles water cools down and sinks (together with salt).
If we had a direct relation between sea surface temperature and salinity, in some region we would need a net flux of salt in the opposite direction to the water net flux.
Global salinity gradients
Global salinity gradients exist. The salinity is above the global mean salinity in some regions -- particularly in warm regions --, whereas in other regions the salinity is below this mean. These salinity gradients are caused by a net loss of oceanic water (evaporation > precipitation + fresh water inflow; enhanced salinity) in warm regions and by a net input of water by (evaporation < precipitation + fresh water inflow; reduced salinity), respectively. These gradients are not related to solubility of salt.