From the point of view of a chemist or physicist, it doesn't make sense. You're using some if the engine's energy to separate water into oxygen and hydrogen, and then burning that in the engine. Since no energy conversion process is perfect, logic tells you that there is going to be a net loss in energy.
It would be like using an electric motor to turn a generator, and then using the electricity from the generator to run the motor. In a perfect situation, you would have a perpetual motion machine, but in the real world, it doesn't work.
I would like to see some real chemical and physical analysis of the "Browns gas" process, and not just some guy on Youtube saying it works. Until then, I remain a skeptic.