'Philbey' and 'Hiro Protagonist' are right I'm afraid
this is because what you are adding to your car is water, which by the process off electrolisis (with power being used from your car engine/battery) is being converted in hydrogen and oxygen gas.
then what happens when you burn the hydrogen it turns back into water water (this is because the hydrogen and oxygen atoms combine with heat, ie burning and produce H2O, ie water)
now the amount of energy required to split up the water molecule is exaclty the same as the amount of energy that is put off when the hydrogen oxygen mixture is burnt and the molecule reforms again.
so even if we assume that the system will run at 100% efficency (which of course it wont, it will never get anywhere near 100%) then the system will still be not acutally adding any energy to your car. And as its not running at anywhere near 100% efficency then all it will be infact doing is putting unecessary strain on your altanator, battery, while still not increasing fuel economy.
note: if you have a tank of hydrogen than this is a different matter, as no energy is required to 'produce' the hydrogen gas. also i have a feeling that a "hydrogen fuel cell" isnt the same as running your engine on hydrogen. Honda have made one, see http://world.honda.com/news/2008/4080616First-FCX-Clarity/ if your really interested, but the idea of a hydrgoen fuel cell, is that its not used in the same way as an internal combustion egnine, but rather to power an electric motor, which will then power the wheels on the car (this 'hydrogen fuel cell car' uses a tank of hydrogen however.)
hope that this helps.