No, Peyton Manning never won a national championship as a college football player.
While Manning's Tennessee Volunteer teams of the mid-1990s were very good, they struggled to beat Florida in the SEC East. Manning lost to the Gators as a sophomore, junior, and senior, which often derailed the Vols' national positioning.
In 1997, during Manning's senior season, Tennessee was in position to win the national championship despite an early loss to Florida. If Tennessee could beat Nebraska in the Orange bowl, and if Washington State could beat Michigan in the Rose Bowl, the Volunteers would likely be named national champions.'
Nebraska rushed for 409 yards and won 42-17. Manning finished second in the Heisman Trophy voting that year; Nebraska split the national championship with Michigan.'