I think the biggest question is fundamentally one of how an alternator works, and I'm willing to be edumacated on that. There is no transmission for an alternator to my knowledge which to me implies that one of two things happens:
1. It runs on demand. When the battery level drops enough to warrant a charge the alternator will flip on, but to save fuel the alternator will turn off between charges.
2. The alternator is on all the time and probably generating pretty much the max output, meaning that a lot of the output could be wasted.
If option 1 is correct, then thermodynamic laws apply. Pick up a book, now put it down. Zero work is done, the book is in the same place, but do it enough and your arms get tired because energy is expended. It's the same principle, 2*H2O + ENERGY --> 2H2 + 02 --> 2*H2O + energy. The net effect is zero and we waste energy doing it (unless we're talking about nuclear reactions, then we can convert some matter to energy but you need a Mr. Fusion and some potassium from a banana peel for that). Here perceived mileage increases are often the result of conscious or subconscious changes in driving habits or comparing the measured new mileage to the EPA estimated old mileage. The placebo effect is indeed a strong one. There's also a good chance that tapping into the air intake or changing things around steals a ton of power and gives an actual mileage increase, but you could save a lot of money by just figuring out what side effect is causing the increase. And then, of course, there's the outright lie factor. If you're selling these you'll of course want to claim large increases and if you've bought one you don't want to admit you were taken.
If option 2 is correct, then all you're doing is converting energy that would otherwise be wasted into fuel and you may see a mileage increase, perhaps significantly. However, there are other concerns:
a. You'll be voiding the warranty of pretty much everything. Adding an explosive gas into the engine will void the powertrain, dealing with water in the engine bay will take care of the electronics, and the caustic bases they require will take care of anything corrosion related.
b. As with the guy with the Lexus above, you'll need to do some fuel management reprogramming to get that working well. With a lot of cars this may not even be possible, I looked into it for mine and a two year LEASE on the computer to program my car would cost $250,000 - and that's assuming I have the skills to make those changes. If this is something that can be tweaked using an ODB connection or if your make happens to still be easy to program you may have better luck.
c. You're reducing the capacity of the alternator. This means you could kill your battery if you've got any high-draw electronics like high beams, stereo systems,and other stuff you'd probably be better off removing if mileage is your top concern, a constant 20A draw is a lot of current.
d. You should also compare the cost and danger to simply swapping out the alternator drive pulley or belt so you can underdrive it, aftermarket performance companies have this because the alternator steals engine power but by sending more power to the wheels you should get better fuel economy. A smaller alternator may also provide even better efficiency at a cheaper price.
e. The main reason the car manufacturers wouldn't use it is because it's high maintenance. Hybrids sell because they don't get treated any differently than cars, you fill them at the gas station, they drive normally, and any routine maintenance can be dealt with at oil change intervals at the dealer. Electrics don't sell because if you run out of juice or forget to charge overnight you call a tow truck and try again tomorrow. Depending on how often this tank needs to be refilled that could be a serious issue, even if it's at fuel up gas stations don't sell distilled water so you'd need to have a reservoir big enough to last between oil-change cycles and I doubt that's practical. Plus needing to handle what's effectively drain cleaner makes it a dangerous no-no from a liability standpoint. I'm assuming that when the tank is empty nothing bad happens, in theory you have two charged plates in a lump of acrylic which is mostly harmless. If there's a chance of overheating and fire when dry, for example if the plates are flexible enough to touch when going over bumps or if the water is needed for cooling, that's another major issue.
This can be made better by allowing the capture and selective release of the gas, much like a battery in a hybrid. But then you vastly add to the complexity and price. If I had a spare vehicle I would be tempted to play with one, but I wouldn't use one on a vehicle I needed as a daily driver.
