Yes, it is in fact possible to generate hydrogen using electrolysis from water. No, it's not currently possible to get enough of it to run a vehicle in real-time with a positive gain of energy. Despite the fact that the best electrolysis systems are only about 70 percent efficient, people are jumping on the hydrogen bandwagon in an effort to improve their fuel mileage, and the systems are starting to move from four-wheeled cars to two-wheeled motorcycles. The first such instance of this was on CMT's Chopper Challenge and now we see a 2008 Kawasaki ZX-10R that's been retrofitted with just such a system.
We can't be sure if the hydrogen for the Kawi is generated on-demand or if it's compressed off the bike, but there's no way that the bike still makes 170-horsepower without a major internal rework of the engine. Hydrogen injection can theoretically improve the combustion of the fuel in the engine but the combustion chamber shape, compression ratio and spark timing need to be optimized to take advantage. Simply adding hydrogen injection without the other changes will not generally have a significant impact on efficiency and will likely reduce the power. The bike will only emit pure water if running solely on hydrogen. If it's mixed with the gasoline, it will still emit CO2 based on the amount of gasoline used. Then there is the issue of on-board hydrogen generation, which consumes energy from the engine and only returns at best 70-percent of the energy put in. In other words, it doesn't work like the builders claim it does.