Turtle, I have used styrofoam balls out of stuffed animals, hypertufa and lots of other stuff. It does weaken the structure but that shouldn't be a primary concern. Using the right material for the job is the trick. People often think 5,000 psi concrete is better than 3,000 psi, or 6,000 psi even better. Bigger numbers are always better I guess is the thinking. But a fake rock normally doesn't need anything like that. Hypertufa structures need very little strength and are normally pretty thick. The important point is it gives a desired look and is strong enough for the task.
I don't think the styrofoam balls really lightened the rocks much and is only good for the first layer because the balls mess up the smoothing process. They use styrofoam balls for some building products but they're really tight tolerances to make a difference.
These days I don't even add mortar clay any more. I just use prepackaged mortar.