This could possibly work.
However, The 50% duty Stan mentions is a very important part of splitting water. As we know when you give a pulse to the inductors a field is created, when the pulse is terminated the field collapses and creates a second pulse. When the pulse given is a 50% duty cycle you will get a better effect and nearly a constant voltage source, but as stan meyer states there is a brief period of off pulse time.
I would not use the 555 as they are nearly impossible to get a 50% duty cycle, and they are not very stable. I would go with a 4046 VCO along with a 10V regulator.
If you want to replicate Stan, I would say you first need a high voltage transformer with dual secondary outputs (no shared ground between primary and secondary), you also need inductors and a good stable 50% duty cycle oscillator to run the transistor and transformer.
Another thing is the importance of gating to prevent the voltage runaway effect. Gating, as stan refers to, is when the off time is greater every X amount of pulses.
_-_-_-_-_-_-_-__________-_-_-_-_-_-_-__________-_-_-_-_-_-_-__________-_-_-_-_-_-_-_________
Look at the above as a sqaure wave, the gated part of this is the flat line and it represents a greater off time. The off time must be great enough to allow the capacitor to discharge, if not as stan says "the voltage will continue to increase until the gas is produced as fast as the water flowing into the cell"
The above pulse train would be the pulse train that powers the transistor and primary winding of the transformer, the secondary part of the circuit pulse train would then look like this.
_--------------------_--------------------_--------------------_--------------------__________---------------------_--------------------_--------------------__________--------------------
Of course these aren't exactly what the pulse trains would look like, but they are a good example.
