Hydrogen peroxide in seawater does lots of different things, some positive and some possibly not so positive, but the Oxydator uses a catalyst to break down the hydrogen peroxide so it may behave quite differently in an aquarium than when H2O2 is simply added to seawater:
The decomposition of hydrogen peroxide by marine phytoplankton
https://pdfs.semanticscholar.org/8888/4098b98540185b606db68197ef2219b0800b.pdf
Hydrogen peroxide is a reactive transient that can be found rather ubiquitously in the surface waters of the oceans at concentrations of 101 –102 nM
Even at its natural concentrations, hydrogen peroxide can still affect the marine ecosystem indirectly by modifying the speciation of trace elements.
...it affects the redox speciation of a number of ecologically important trace elements, including iron (Moffett and Zika, 1987; Millero and Sotolongo, 1989; King and Farlow, 2000), copper (Moffett and Zika, 1987; Sharma and Millero, 1989; Millero et al., 1991), chromium (Pettine and Millero, 1990; Pettine et al., 1991) and arsenic (Pettine and Millero, 2000). The speciation of these trace elements affects their biological availability and/or toxicity and, thus, their influence on the behavior of the marine ecosystem.
The sinks of hydrogen peroxide in the oceans have not been as well studied as its sources. The contribution from its chemical auto-decomposition is minimal to negligible
The major sink of hydrogen peroxide has long been suspected to be its biologically mediated decomposition