do the roman numerals follow throughout the whole year
Yes.
We have:
Styczeń = January = I
Luty = Februrary = II
Marzec = March = III
Kwiecień = April = IV
Maj = May = V
Czerwiec = June = VI
Lipiec = July = VII
Sierpień = August = VIII
Wrzesień = September = IX
Październik = October = X
Listopad = November = XI
Grudzień = December = XII