No, because no rookie quarterback has been to the super bowl.
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There have been 8 Super Bowls that the Steelers have played in. They have had 3 different QB's in those games. Terry Bradshaw was the starting quarterback for the Steelers dynasty in the 70's, where they won all 4 that they went to. 1975 (SB9), 1976 (SB10), 1979 (SB13) and 1980 (SB14). In 1996 (SB30), Neil O'Donnell was the quarterback for the Steelers loss to the Dallas Cowboys. Ben Roethlisberger was the quarterback for the Steelers in their wins in 2006 (SB40), 2009 (SB43) and their loss in 2011 (SB45).
No quarterback has ever won a Super Bowl with two different teams. Craig Morton started for the Dallas Cowboys in Super Bowl V and Denver Broncos in Super Bowl XII, losing both games. He remains the only QB to lead both an NFC and AFC team to the Super Bowl. It wasn't until Super Bowl XLIII that another quarterback arrived at the Super Bowl with their second different team. In that game Kurt Warner led the Arizona Cardinals (in a losing effort) after previously leading the St. Louis Rams to Super Bowls XXXIV (win) and XXXVI (loss). Incidentally, while 5 different men have lead two different teams to the Super Bowl, no head coach has ever won Super Bowls with two different teams either. The head coaches that have led two different teams to the Super Bowl are: Don Shula (Colts and Dolphins), Dick Vermeil (Eagles and Rams), Bill Parcells (Giants and Patriots), Dan Reeves (Broncos and Falcons), and Mike Holmgren (Packers and Seahawks). All 5 coaches have Super Bowl rings. Shula, Vermeil, Parcells, and Holmgren got their rings by winning the Super Bowl as head coach, while Reeves got his ring playing for Dallas (Super Bowl VI champion).
Los Angeles/St. Louis Rams. The Rams lost Super Bowl XIV, won Super Bowl XXXIV, and lost Super Bowl XXXVI for a record in Super Bowls of 1-2.
Only the 1972 Miami Dolphins have won a Super Bowl with an undefeated record.
The 2007 Patriots went undefeated for the entire season until they lost the Super Bowl to the Giants. Unless you meant to ask what team has the best win-loss record in the history of the franchise, but has never won a Super Bowl, that would be your answer.