You are correct. Katarzyna is the Polish name for Katherine.
I'm also researching Kaczorowski, as this is my mother's maiden name. Her father was Vincent Francis, Jr. His father was Vincent Francis, Sr., from Brzezno, Plock. His father was Ignacy Kaczorowski.
My grandfather was born in the Philadelphia area, (their port of entry, I believe) after his parents immigrated to the U.S. from Poland.