No it's not suitable for your car battery.
Water that has come out of a de-humidifier has been in contact with a heat ecxhanger so therefore cant be classed as distilled... it certainly has no acid in it.
Distilled water is water that has many of its impurities removed through distillation. Distillation involves boiling the water and then condensing the steam into a clean container.
The manufactures of steam irons recommend that you don't use it because it cac contain many dust particles whih are decomposes by bacteria to form a weak organic soup which can in extreme case cause brown stains.
I buy the cheapest bottle of water in Tesco's for my steam iron, around 25p, and it seems to work OK. At least it doesn't clog up the iron and the bottle lasts for a few weeks. I save it if there is any left over as well for next time. Well there is a recession on !
I use water from my dehumidifier in my steam iron without any problems. I do it because where I live the water from the tap is so hard and would soon ruin an iron.
But I'm not so sure that I would use it in a car though, because as other posters have said, it's not really pure distilled water.