No. Water stains are scars on the fence and penetrate deep into the grains of the wood. Cleaning and staining the fence will improve the appearance but will not remove them. They will be visible after your fence is stained.
To answer your question we remove post per post to which the fence will never be down. It should never be down nor should it be power washed due to the high pressure that will scar and splinter it. We prefer using a hydro caloric solution to remove the mildew on the fence using 40 to 60 PSI equivalent to a garden sprayer and then staining it with an oil base stain.