kivig:
Is static charge dangerous to the board in situations like this?
Static discharge is always a concern.
But keep in mind that static discharge is relative to the same thing that all voltages are relative to... COMMON. Aka, Ground.
As already mentioned, if your circuit was actually connected to EARTH ground then you would have a very well known common / GROUND connection.
I think it is very likely that one side of your circuit would have higher potential than the other, due to the polystyrene. In which case, a voltage potential could develop between the sides of your circuit.... allowing an electro static discharge to, well, discharge. You need to carefully ensure your entire circuit's common / ground is at the same potential at all times.