Not really. It's a matter of drilling carefully:
http://geography.about.com/library/misc/ucghyben.htm
"On low, small islands that are largely composed of coral or other porous materials, salt water intrusion into the underlying interior is quite common. The drilling or digging of wells on these islands and especially on along the shoreline must be done with care [emphasis added]."
Notice that the author didn't say "pointless."
Most reasonably-sized islands have a subsurface fresh water source. The presence of salt-intolerant trees tells you there's fresh water available beneath the surface.
> ... assuming you can get at it in a useful quantities, will need a lot of processing before you can use it.
If that were true, it would kill the trees. I know a number of locations in Alaska near salt water where, because of geological changes resulting from the 1964 earthquake, even though the surface is dry there's no subsurface fresh water at all, and all the trees promptly died. Those locations are rare.
It's not nearly as simple as drilling a well far from salt water, but it can be done.
