I think in Ghyben-Herzberg equation by going farther from the shoreline the water-level and interface level approach a constant value. It is in theory, but for the real cases it depends on the whole system setting and the rate of fresh water discharge toward the saline water body and other factors.
intuition says that the relationship will break down when the interface approaches the maximum depth of meteoric water circulation in that region, allowed by the geological structures.
It is a very important question, Pl. see our recent study in coastal sandy aquifer (Hydrological Science Journal 59(12) 2014), though the groundwater levels are going down to 4 to 5 m below mean sea level, still the aquifer is producing the very fresh water. Hence, I feel that the Ghyben-Herzberg equation works only in certain conditions.