Git stores every version of a file as distinct compressed copies (objects). Periodically, it packs these objects into a pack file. To save space, delta encoding is used in this process. As far as I recall, this is done on a line by line level. In this case, simply dumping this JSON data is going to hamper the delta encoding and the repository will grow substantially in size each time there is a change in data.

Then there's the issue of retrieving the data. The basic implementation of reading objects using git checkout and rewriting the objects to disc but there are other ways to read the raw file contents into memory and do your stuff there.

It's not going to be the most performant or best way of version controlling data but in many cases it will do a decent job.