I've never played Deal, Sandwich, Prince's or Littlestone (the other links in the vicinity) when they've been really really baked out. I think each has fairway watering, so getting that dry would be dependent on the course manager keeping the water turned off despite a long period of hot, dry weather.
Adam,
I don't believe Littlestone has fairway watering and, therefore, is drier than the others, so you can enjoy watching your ball skitter off and disappear in its jungle-like rough!
Rye does have fairway watering but once the new grass is properly established it will be used sparingly, I am told. In addition, now that the sea has retreated, the wind does not blow sand across the old course fairways any more, so hundreds of tons of sand is being spread to replicate their old character. Fortunately, Rye has its own supply of beach sand.
Sam