My great-grandfather, as well as all of his brothers and any spouses, came over as adults. I don't know if it was all at once, or over a period of years. Some of them had children born in Poland, while others were born in the U.S. Their parents remained in Poland. I don't know if their parents had relatives with the same surname. Of course, this was over 100 years ago. In the interim, Poland has been involved in two World Wars, and three regional wars, as well as 50 years of Communism.
Maybe It was changed a bit already in USA ?
To the best of my knowledge, Balitewicz is the original spelling.