They don’t say what foam it is. At least some foam core board, such as Gatorboard, uses polystyrene foam. That can stink to cut but doesn’t contain halogens like chlorine or fluorine. Can’t speak to dyes that might be used in the backing for the foam core. Gatorboard uses melamine in the backing which as far as I know doesn’t produce fumes that would damage the laser. I would sure want to vent fumes from cutting both, though!
Since they don’t say anything about what it’s made of, I would say it’s a bit of a gamble but at the same time Gatorboard is probably the benchmark for foamcore.