Let's see. 12 volts and 1.8 watts means 150 milliamps.
The float charger for my motorcycle is 800 milliamps.
The average car battery is around 60 amp-hours. So, to fully charge a car battery with this would take 60/0.15 hours, or 400 hours. Granted, it would take my little float charger 75 hours to restore that same completely dead battery. This is why bench chargers are usually at least 2 amps and often 10 amps (a 2 amp charger would take 30 hours and a 10 amp charger would take 6 hours).
The little solar thing won't be useful for restoring a dead battery, but if you have a car that will often sit for several weeks outside without being used then it might be useful as a trickle charger. Even though it doesn't seem to have the intelligence to know when to stop charging, the extremely low 150 milliamp current isn't likely to fry a battery.
If you want a bench charger, Sears has some nice options that are "intelligent" chargers that will turn off instead of overcharging (though they aren't meant to be dedicated float chargers) and I've always had good luck with Sears. Alternately, if you are looking for a float charger, the Battery Tender brand comes highly recommended and Summit Racing has an excellent online presence as well as a stellar reputation (and prices that are lower than brick and mortar stores even after shipping is factored in).
I may be biased though since I own a Sears brand bench charger and the 800 milliamp float charger is Battery Tender's waterproof model that I bought through Summit.
ZV