I do not think it would be a good idea at all to use styrofoam to grow in. Some plastics and petroleum based products can have very bad chemical reactions when they come in contact with certain other products and such. Take a Plastic bath Shower surround. If you use the wrong glue, it will have a chemical reaction and start to melt. Take a styrofoam cup and pour gas into it. The cup will not even slow down the gas from hitting the floor. Which makes me think that adding some chemical Nutrients could possible also have a adverse effect on the cups.
Now I am not sure of this happening. But seeing how the styrofaom can have a chemical melt down with one substance makes me wonder if there might be others.