Not if your son is of school age and has to be put in an English-medium school. A good school can cost more than 4000 PLN a month. Also, not if you plan on saving up for college or retirement. Even if your son receives free schooling, you're not going to be able to save very much more than a very modest rainy day fund. Those are the two biggest problems ex-pats face in Poland: tuition for school-age children, and a very, very low savings potential.
To give you an idea about costs, a modest two-bedroom apartment will set you back 2500 to 3000 PLN a month, all inclusive (rent, fees and utilities without internet/phone/TV). Food and general household expenses for three people is going to come to 1500 to 2500 PLN, depending on how frugal you are. Less if you prepare all meals at home from scratch using in-season local ingredients. More if you like beef, seafood, or prepared or foreign foods, or if you eat or snack away from home a lot.
That's a minimum of 4000 PLN right there. Then there's clothes, travel, entertainment, etc. As well as the cost of your relocation to and from Poland which has to be added in (tickets, visa, residency permit). That will leave you with only a pittance to save, if anything at all. And that's without taking into account schooling/daycare for your son.
6000 net a month is a rather modest existence for a young, single ex-pat, a frugal existence for a couple, and not even worth considering for a family.