At the risk of sounding like an idiot, would there be any value in capturing some of the energy as compressed air/purified oxygen to be injected in to the hydro

At the risk of sounding like an idiot, would there be any value in capturing some of the energy as compressed air/purified oxygen to be injected in to the hydrogen burning process... thingy? Perhaps in a manner similar to how a SABRE engine works? [0] [0] https://en.wikipedia.org/wiki/SABRE_(rocket_engine) https://en.wikipedia.org/wiki/SABRE_(rocket_engine)