There could be, if "desert island' were used to refer to an island in a desert climate, like Socotra. But as it is, "desert island" is used to mean the same thing as "deserted island" and they are thus synonymous. It seems to hark back to an older use of "desert" not meaning "hot, arid climate" but meaning "wild and uninhabited".
How can you have both a dry climate and a wet one and still call both a desert?
a:arid land with usually sparse vegetation; ... and b: an area of water apparently devoid of life
In addition, the definition of "island" is: " a tract of land surrounded by water and smaller than a continent, so how can the second definition of "desert" apply?
Harry 