I wouldn't choose ivy. Lamium maybe, or Liriope if it's hardy where you are.

I live in South Carolina

Yeah, skip the ivy. English ivy is considered an invasive species in both of the Carolinas. And it would devour stepping stones in a blink of an eye!

Instead, look for some other low growing, shade tolerant evergreen groundcovers like the two mentioned previously.

In other words choose a clumping kind that won't repeatedly send shoots or runners across the rocks. The liriope for instance. Also it works better to install a continuous path with something like pavers that touch one another. Because with spaced out stepping stones a body always has to watch where they are stepping.

There are many kinds of ivy.

Part of the problem with the picture provided is that we see not surroundings, but only the target area. Surroundings would be as important a factor in deciding what to do.

To answer the question, yes, ivy -- English ivy -- is used as a groundcover in many places in the South. It is aggressive and has worked out best only for sizable areas, it's not the kind of groundcover one would use in a small space (though I've seen this done many times in Atlanta area. It works but it's just more maintenance.) I would not consider starting ivy here, where it does not already exist. But if this area is close to a neighbor's property, and they already have English ivy at their perimeter, adjoining yours, then there would pretty much be no other practical alternative. To introduce another groundcover would mean an endless fight between the two plants in which the eventual winner would, with near certainty, be ivy. So assess what's growing on the other side of any nearby fence before making your decision. If you used 2' stepping stones, there would be a monthly trimming to keep ivy off of them..

I love a solid bed of Liriope, but it is not a good choice if one intends to walk in the bed, even with stepping stones. Something much shorter, like dwarf mondo, would work out better.

I would make the walk solid pavers, and yes to liriope. It comes in both solid and varigated. Beautiful flowers in late summer. Easy care. Once in awhile, cut back in late winter.