'Rashi': No. He was exiled in the days of Yechanyah, and never served as Kohen Gadol. It says "Yehoshua ben Yehotzadak ha'Kohen ha'Gadol", i.e. Yehoshua was Kohen Gadol in Bayis Sheni, when he returned from Bavel. He became Kohen Gadol before his uncle Ezra ben Serayah, for he returned with Zerubavel before Ezra returned.