Les drank a lot of coconut on a couple of his shows; he didn't seem to get ill.
I would definitely rather have plain water and if need be I would begin digging up along the beach to find water. I have read that if you dig behind the first row of dunes you will get water without the salt; I have never confirmed this.

Perhaps another way would be to scavenge some trash and build some sort of still to remove the salt. This would take some thinking about but I am sure that on every island in the world there is trash that has floated there.