[Gen III] Shiny Hunting legendaries

This is regarding shiny hunting in gen 3, so my Sapphire and Emerald copies have a dry battery, and I'm wondering if using the run away method for catching Rayquaza in Emerald and soft resetting for the Regi's in Sapphire are actually worth doing or the dry battery has any affect as to the outcome of the shinies. I'm roughly aware of the RNG problem Emerald has but I have heard online of people getting a shiny Rayquaza using the run away method with a dry battery