With 1/2" backer board or 5/8" Advantech to distribute the loads over the foam and a slab to fully support the foam, it's a more rigid structure than wooden subflooring on joists. The slate itself can be pretty structural at 3/8" or thicker too.
You don't need many tapcons to keep it from moving- 16" o.c. along the seams would be plenty. Lap the backer-board seams by at least a foot with the foam seams to avoid any edge-rocker developing over time.