I say a big NO.
Without getting too complicated, When H2O2 is dissolved in a water it losses an Oxygen atom (That becomes a free radical). Free Radicals like to "attach" themselves to other particles. In the case of living things "attach" may just as well read "KILL". This process is the same process that causes Iron to rust!!!
Yes it will Kill any nasty things in your root zone, but it will also kill all the good things, and worse of all weaken your root system, which is a precursor to numerous problems in itself.
As for Oxygenation almost all of the oxygen ions released when adding H2O2, will actually attach themselves to something before your root system can even imagine absorbing them.