Are you going to visit relatives? I ask because that's probably your best bet for getting access to the Polish countryside. I'm no expert, but most of it seems to be (peasant) farmed and whilst there is plenty of woodland, much of it seems to be controlled by hunting cooperatives who maintain the environment. They have a sort of forestmeister system like the Germans my cousin is one, and Ive been out shooting with him (we only got mushrooms!). I doubt there would be any problem camping but they might not be keen on your cutting wood or building fires on their patch.
Anyway, relatives/friends/work colleagues are bound to know someone who hunts and might be prepared to take you out but dont expect them to speak English!
There is wild mountain country along the Tatra mountain chain between Poland and the Czech Republic, but I think the wildest country is on the Eastern borders. From what understand, there is no way you will be allowed free access to the Bialowieski National Park.
If it helps, Woodcraft school apparently do a course in Poland:
http://www.woodcraft-school.co.uk/tracking-in-poland.htm
They might be able to give you some advice.
I dont know if this helps at all, but good luck

and please write a report when you get back. Id like to do some of that myself, but so far have not been able to escape the kind hospitality of the (very) extended family!
Ted W