I've used H2O2 to remove IRB in a water heater, and it worked well, although it was a nuisance to keep re-treating. It's commonly used to treat wastewater in commercial or municipal systems.
The EPA says (http://iaspub.epa.gov/tdb/pages/trea...tOverview.do): "Hydrogen peroxide (H2O2) is rarely used in drinking water treatment as a stand-alone treatment process. H2O2 is a weak mirobiocide [sic] compared to chlorine, ozone, and other commonly used disinfectants. Consequently, it is not approved by regulatory agencies as a stand-alone disinfection treatment process." I'm not sure why they say it's weak compared to chlorine, because H2O2 is a more powerful oxidizer than Cl, at least in their pure forms (which are rarely used).
One on-line vendor who sells H2O2 systems (http://www.cleanwaterstore.com/peroxide-iron-filters.html) says "Hydrogen peroxide (“H2O2”) is a powerful oxidizing agent, much more powerful than aeration, chlorine or potassium permanganate." They use a 7% H2O2 solution. They also say that you need an activated-carbon filter following the H2O2 system to remove the oxidized gunk, as do chlorine-based systems.
To answer your question, IMH(non-professional)O, it won't do anything softener-wise, and wouldn't be much better purification-wise than chlorine, which is very commonly used. I do know water treatment pros who despise chlorine for various reasons, however; they would probably prefer H2O2. All in all, I would only use it on a whole-house basis if there were a disinfection need only, and would follow it with GAC. It looks like the ongoing maintenance cost of H2O2 is also significantly higher, but I may be wrong -- it depends on injection rates of the $15/gal H2O2 vs $3.29/gal Ultra Clorox.
I'd be very interested in your experience with the system.