No, Justified Image Grid by itself is not a source and it's not another gallery management plugin. It uses Sources you know and probably use. Album-gallery relationships are already available using excellent solutions without much to improve upon, thus JIG didn't intend to re-invent the wheel.
To have Album-gallery relationship, you need to use:
- NextGEN Gallery
- Facebook overview (single-level)
- Flickr Collections (multi-level)
- It's also possible using the Recent posts source. Album or gallery cover would be the featured image of a post, page, or custom post type. The photos would be placed as a JIG gallery in the post content.