In short, yes. The Babylonian exile did not encompass all the Jews in Judea. From Stern, Ephraim (November–December 2000). "The Babylonian Gap". Biblical Archaeology Review. 26.

"From 604 BCE to 538 BCE —there is a complete gap in evidence suggesting occupation. ... I do not mean to imply that the country was uninhabited during the period between the Babylonian destruction and the Persian period. There were undoubtedly some settlements, but the population was very small. Many towns and villages were either completely or partly destroyed. The rest were barely functioning. International trade virtually ceased. Only two regions appear to have been spared this fate—the northern part of Judah (the region of Benjamin) and probably the land of Ammon, although the latter region awaits further investigation."