No, silver tarnish will not harm fresh water pearls. Time will eventually cause the sterling silver to tarnish and the way it is cleaned needs to be a careful procedure to avoid damage to the pearls. Several gentle methods will work; use an ionic cleaner such as the Speed Brite, use a baking soda/aluminum foil/hot water bath, or a silver polishing cloth. Do not use toothpaste as it has abrasives that can leave fine scratches on the silver and destroy the nacre on the pearls. Or upgrade the sterling to Argentium to enjoy longer periods of time between cleanings.
Answer contributed by Dale `Cougar` Armstrong