I'm not sure that would help. H2O2 is very interesting, but not many sites recommend using it to kill bacteria. US Peroxide is one of the largest manufacturers of H2O2, and their applications regarding H2O2 used with drinking water are to destroy the ozone used to disinfect it. See
SURFACE WATER TREATMENT
Taste & Odor Removal / Ozone Enhancement
Residual Ozone Destruction
Also, natural sunlight generates H2O2 in water due to the UV energy. See
Safe - Despite its power, H2O2 is a natural metabolite of many organisms, which decompose the H2O2 they produce into oxygen and water. H2O2 is also formed by the action of sunlight on water - a natural purification system for our environment. Consequently, H2O2 has none of the problems of gaseous release or chemical residues that are associated with other chemical oxidants. And since H2O2 is totally miscible with water, the issue of safety is one of concentration. Industrial strength H2O2 is a strong oxidizer and as such requires special handling precautions.
Versatile - The fact that H2O2 is used for seemingly converse applications proves its versatility. For example, it can inhibit microbial growth (as in the biofouling of water circuits) and encourage microbial growth (as in the bioremediation of contaminated groundwaters and soils). Similarly, it can treat both easy-to-oxidize pollutants (iron and sulfides) and difficult to oxidize pollutants (solvents, gasolines and pesticides).
Selective - The reason why H2O2 can be used for such diverse applications is the different ways in which its power can be directed -- termed selectivity. By simply adjusting the conditions of the reaction (e.g., pH, temperature, dose, reaction time, and/or catalyst addition), H2O2 can often be made to oxidize one pollutant over another, or even to favor different oxidation products from the same pollutant
It does say H2O2 can be used to control, or to stimulate microbial growth. So you would have to figure out which you want to do, and what it takes to accomplish it.
But it looks like you don't want to add H2O2 upstream of the ozone injector to prevent destroying the ozone, and just let normal UV radiation from the sun make it in the pool. Regards,
Mike Monett