I suppose it would depend on what it was made of...do you have any more information ( manufacturer, links to info, etc.) about it?
Most aquarium decorations at the LFS that look like stones could be considered "simulated stone"...so I guess I don't know what your specifically talking about.
I could be thinking of something totally different, but isn't that usually made out of fiberglass? I'd be curious about what they used to paint/dye it, but certainly fiberglass would be harmless.
Those gaming figures and "collectibles" such as anatomically correct mermaids are generally of cast resin painted with acrylic. Acrylic is safe: essentially, once it's cured, it's a thin film of acrylic plastic. But with prolonged submersion, I think it would tend to flake and lift. The cast resin used is a two-part resin. Those are inert once they've completely cured.