NO - FOOD GRADE DOES NOT HAVE STABILISERS - Food grade hydrogen peroxide is generally a 35% dilution, compared to the 3% to 5% hydrogen peroxide that you can get at the chemist, and the chemist usually does not sell Food Grade but rather BP grade Stabilizers like phenol, sodium stannate, tetrasodium pyrophosphate, and acetanilide are said to be found in regular over the counter hydrogen peroxides.
Some of these stabilisers in BP grade are said to have these stabilisers and can be bad for your health.
Best suggested that you do your own research and make an informed decision. This article is based on research done regarding the various hydrogen peroxides and their uses.