No, reverse osmosis can not/does not remove all the dissolved chemicals. Distilled water always removes all dissolved chemicals. "Catch" rain water can be used since it has been distilled (evaporated) naturally by the sun.
Go buy yourself a gallon of distilled water at the supermarket for $1.50. That's a heck of a lot cheaper than getting stuck on the road and then having to buy a new $80 battery. (Plus any towing cost, then mechanics charges.)
The moral of this is: Don't screw around with strange sources of water for refilling your battery. If you are on a boat then get a rainwater catch device if you can't buy distilled water. All bottled "drinking" water, like Perrier, natural spring water etc., etc., have dissolved chemicals that will destroy your wet lead-acid batteries.