NO. every quarterback in the superbowl has thrown for at least one touchdown. There hasn't been one who has done that up to this point if there is then this answer will probably change...
The first touchdown thrown in Super Bowl 44 was thrown by Peyton Manning to Pierre Garcon in the first quarter.
Kerry Collins
3
Brett favre
Joe Namath of the New York Jets in Super Bowl III.
The Dallas quarterback with the most interceptions in a career thrown in the super bowl is Roger Staubach with 4.
kerry collins
Bob Lee was an NFL quarterback who played in two Super Bowls and threw a touchdown pass in Super Bowl XI.
Jimmy Cefalo caught the only offensive touchdown for the Dolphins in Super Bowl XVII (1983), from quarterback David Woodley. The Dolphins lost 27-17 to the Washington Redskins (Washington's first Super Bowl win).
Tom Brady
Not in Super Bowl XVIII but I remember a couple of TD passes thrown by non quarterbacks. Running back Lawrence McCutcheon of the Los Angeles Rams threw a TD pass to Ron Smith in Super Bowl XIV and running back Robert Newhouse of the Dallas Cowboys threw a TD pass to Golden Richards in Super Bowl XII.