I believe so - I was recently reading something similar and although I can't recall the specifics, there was mention of the VAT being payable at the Customs terminal in Swiecko.
I belive that you do not. Germany is the only country that I know of which enforces this. See this on european vat tmf-vat . com which talks about the details. The rest of Europe, including the new countries were treating this as international passenger travel so exempt. I think like all eu vat, this was up for review.