Not exactly. The critical thing for a ghost swirl is to create a situation where parts of the soap can turn liquid (gel) while other parts of the soap stay solid.
Any set of conditions that causes a block of soap to do this will work. It just so happens the easiest way to get a swirly effect is to play with variations in water content while controlling the temperature of the soap.
Soap with more water tends to turn into a liquid (a gel) at a lower temperature. Soap that gels looks more translucent and deeper in color.
Soap made with less water won't become a gel until it reaches a higher temp. Soap that doesn't gel looks more opaque and lighter in color.
This differences in the gelling temperature is why the ghost swirl happens. But it won't happen UNLESS the overall temperature of the soap rises above the lower gel temp AND stays below the higher gel temp. Regardless of water content, if you cool the soap sufficiently, it won't ghost swirl because none of it gels. If you CPOP at 170F for sufficiently long, the soap won't ghost swirl because all of it gels.
Think about the bullseye look of a partial gel. The center of the soap gets hot enough to turn liquid (gel), but the edges stay cool enough so they stay solid. This is an example of the "ghost swirl effect" in a soap with a constant water content. Not a very pretty look and not very swirly, granted, but the conditions that trigger this are the same as for a ghost swirl.
When I've done a ghost swirl, the soap doesn't look like it obviously is in gel, because a lot of it isn't liquidy. The parts that gel are just thin layers between layers of solid-ish soap. The overall effect is that the soap appears like it's not gelling.