A local area that's low like your thumb in the grout joint won't matter at all with the foam and board. It's the local high spots that you need to think about. I can't tell from the picture if it's a little area that's 1/4" high.
I've used the leveler but I'm not a big fan of it for leveling local areas that vary by more than an 1/8" or so. The stuff can fracture if it's thicker and not contained/restrained. It's best if it's filling a thin low spot, and then something is adhered on top of it, like tile or vinyl flooring.
I also haven't used the leveler where the weight on it would be high. I think that if you use the leveler you'd still be best off with a stand bottom that consists of a continuous sheet of 3/4 plywood so the load will be more or less evenly-distributed across the surface, approximately 1.5 psi, which really isn't much.
That stone looks pretty strong. It doesn't look like the slate I've seen with thin, brittle layers that flake off occasionally.
Using the right foam won't mess up your stone.
