and have never heard of it before, but I do have a few thoughts that immediately came to me.
Hydrogen Peroxide is not very good as an anti-bacterial agent, and it does a lot of damage to living tissue...even when we use it on a cut, we often have damage to the edges of the cut. So I would wonder if it would do further damage the roots. Actually, you don't know for sure that you have any damage to the roots, do you?
Another thing, I would expect that any action that you would get from the H2O2 would be at the surface of the soil where it first comes into contact, and would not get to the roots.
Then there is the good bacteria in the soil that helps the plant....would it harm them as well if it does get down to the roots?
If I were concerned about the watering, and if I were over or under watering the plant, I would get a gauge so that you know when you have to water. I do know that all of my indoor plants suffer in the winter----not as much daylight, the air too dry because of the furnace, etc. But I just accept that where I cannot avoid it, and look forward to summer with conditions that make my plants happy.
On edit: With all that said, I do not think that the concentration that you are talking about would do anything, good or bad.