the best answer I can provide for the OP is: it depends on the soil and the de-salting method. The more clay is in the soil, the more difficult it will be to remove the salt.
If I wanted to prepare a previously such a piece of land for agriculture (garden or farm), I would prepare myself for some really hard work, to begin with. I would also resign myself to the fact that it might take several seasons to get the land to the point where it could be arable
I would first look at the soil composition itself. Some types of clay become impermeable to water with much lower concentrations of sodium, and rain can obviously wash salt rapidly out of permeable sand.
I would start with soil amendment. If the soil had a high clay content, then I would add organic material (loam, composted organic matter, manure from grazing animals, etc) and mix very well. I would then irrigate with the intent of washing the soil. Irrigation water, whatever the source (rivers, ponds, municipal sources, etc.) may contain some salt, and if not drained properly, will deposit the salt and other minerals upon evaporation.