Dorymae -- If I'm following you correctly, I think the article might imply that soap that gels does crystallize and soap that doesn't gel does not crystallize. If so, I don't think that's what Clara meant, although I can see why people might pick up on that incorrectly. Soap crystallizes, meaning it creates some kind of orderly structure, whether it gels or doesn't gel. The kind of crystalline structure might be different for gelled soaps vs. not-gelled soaps, but there's a crystalline structure.
Here's an analogy: One end of each soap molecule is positively charged (the sodium Na end) and the other fatty-acid end is negatively charged. Think of each molecule as a kind of magnet. Magnets really desperately want to align themselves so the north pole of a magnet is near the south pole of another. Soap molecules are a bit like magnets -- the sodium end of one soap molecule wants to be next to the fatty acid end of another soap molecule so the electrical charges are evened out.
Since there are a bazillion soap molecules all seeking the same kind of electrical nirvana, they solve this problem by organizing themselves into a variety of interesting shapes -- sheets, balls, cylinders -- that allow the sodium ends to face toward the fatty acid ends, rather than be all jumbled about in a random mess. This orderliness is the crystalline structure I'm talking about. Gel might make all these soapy gymnastics easier, but even without gel, the soap molecules are going to create some kind of orderly structure that makes them "happy". It might take longer, but they will figure it out eventually.
The physical hardness of a soap is more determined by the amount of water used to make the soap, all other things being equal. According to a study done by Kevin Dunn, higher water soap is softer at the time of unmolding than lower water soap. As the soap cures, the higher water soaps will become about as hard as the lower water soaps, so the difference between the soaps gradually evaporates (pun intended) with time.