You can probably do it without any problems on an ink jet providing that:
1) The sheet styrene has a slight amount of texture to the
surface. Ink can't soak in at all so some texture will kee the
ink from just wiping right off.
2) The printer is capable of feeding heavy sheet stock (most of them
feed it in the front and straight out the back without doing much
"Rolling" of the paper)
A laser probably won't work as there is most likely too much heat in
the fuser section. The fuser actually melts the toner particles
so that they bond to the paper. Not a good thing with meltable
styrene sheets.