Sure, you can always use an external power supply to separate H2 for use in an engine, just like you could use one to provide H2 for a fuel cell or use an external energy source for power to charge a battery (e.g., plug-in hybrids). The laws of thermodynamics (that these folks are ignoring) are applicable to closed systems, without external energy inputs. The problem is trying to use energy from the engine to produce H2 from water and them extracting the energy from the recombined (combustion) water, this is clearly a violation of the first law of thermodynamics.

The energy required to separate the H2 is exactly the same as the maximum energy that can be recovered by recombining the H2 into water during the combustion process, this is not due to the inefficiency of the engine; it is a fundamental limitation of the physics.

I am not saying that the use of H2 to somehow change the combustion characteristics of the internal combustion fuel is impossible. Someone might be able to design an engine to run more efficiently on a modified fuel that uses H2 as a component, just as you can design a more efficient engine to run on higher octane gasoline (at the expense of some higher emissions). However, that is not a "bolt-on" modification; it is an alternate engine design (i.e., higher compression, different timing, modified fuel injection, etc.) using a fuel with different components/additives (and probably worth some serious research). In that case, it would probably not make sense to use the engine power to produce the fuel "onboard" the car anyway. Then, we are just talking about the cost/benefit of reformulated fuel for use with a modified engine design (not unlike flex-fuel engines that are designed to run on E85).