Yes. Deionized water can be used as an alternative to distilled water since deionization removes all salts from it. Such water if passed through proper filters before bottling and free from heavy metals, dirt and fungus is equally safe for batteries and even could be used for drinking. So if you wish to go for deionized water then choose a good brand and make sure manufacturing date is labeled on the bottles to let you know how old the water is although water age does not matter if the purpose only is to fill batteries. Do check that bottled deionized water is free from white or green substance as that could be bacteria, fungus or some other microorganism. [White substance could also be settled salts if water was not properly deionized or it may be tap water with fake “deionized” label on it]
Deionization is an ion-exchange chemical process that uses ion-exchange resins. There are usually two deionization methods employed, one is co-current and the other one is counter-current. Compared to co-current, counter-current method is preferably used as it is low cost, faster deionization method that also produces high quality deionized water. Mixed bed deionization is another technique for producing very high quality deionzed water but since the process is slow and cost more it is not usually used for producing water at commercial scale. Instead counter-current method is commonly used to produce affordable deionized water in large quantity for selling.
Wet batteries (also flooded batteries) use water mixed with sulfuric acid as an electrolyte. These are not sealed or valve regulated batteries thus these also lose water over time since it is evaporated through vents in caps of individual battery cells. Topping them up in timely manner is necessary to maintain electrolyte level in batteries and not letting the battery plates go dry. Make sure to use distilled or deionised water to top up your batteries. Avoid using tap water in all cases since tap water is full of minerals, dirt particles and fungus spores that can damage your batteries in no time. Also make sure that electrolyte level should never go below the “Low” mark on your battery as that could cause battery plates to start drying up from the top. If battery plates go dry, these are irreversibly damaged.