From what i understand the use of H2O2 from the book of Aquarium Fish Disease, and one of the Amano's books that given a small dosage of H2O2 will dramatically increase the oxygen level, and this will affect the algae, hence kill them.
If high enough dosage is given, I am sure it will affect the bacteria in filter, but if you're worried about that, just turn off the filter for a hour or two, with the light on, H2O2 will turn into oxygen and water very quickly. I would also house the fish somewhere else during treatment if I plan to use high dosage.