This idea was originally toyed with as an experimental way of minimizing js/css payloads. (Which is of course kind of neat, but in practice you should get better benefits from just minifying and gziping content.)
It does work as a way of storing arbitrary data on a forum, but would probably be too difficult for an average user to generate a reasonably compressed image. http://iamcal.github.io/PNGStore/
If someone provides the code to generate a standard json file structure for a game (probably hosted on a jsfiddle type of site for collaboration and ease of use to run), a completely client side solution wouldn’t be unreasonable. For example, just Base64 encoding the serialized json and then creating an image element with the data as the source. You could them prompt the user to drag and drop this file, or you’d have to bounce this off a server to get an automatic file download. Base64 encoding of course inflates the file size, but we’re not storing much data anyway so it doesn’t matter.
In any case, by the time you get to level of complexity, it may be worthwhile just setting up a proper web app which can track the characters, stats, purchases, missions, and trades etc.