Yes. Anywhere there's water, there's the possibility of distilling it provided you have the materials. You'll need a heat source, container for boiling, some type of collector and a condenser to condense the steam back into water. Unfortunately, that stuff may not be on your island. The best bet would be to go to the center of the island and try to dig down to water or look for another natural source like rain puddles, ponds or streams but remember, there's a high probability of parasitic infection drinking from standing water pools.
It would probably take far too much wood (fuel) to condense enough water to sustain yourself without proper equipment though. Probably not the best method if you're randomly stranded.