Hi - thanks for posting with the photos. Collectors refer to "battery jars" rather than "battery acid case" - I changed the post title in hopes that someone else may stumble upon this and be able to help.
My first reactions:
Yes, it does look like a battery jar, although I cannot say I have seen one with a square cross-section like this.
Appearance-wise, it looks much newer than any battery jar that I have seen, but perhaps the use of glass for certain specialty jars continued far longer into the 20th century than I realized. We are all now used to seeing lead/acid batteries in plastic containers - ie. those used in autos.