No, we most likely would not have leapt them, especially with their still playing in the Sugar Bowl that year being due in part to their winning the SEC Championship...over a #11 ranked Alabama, not an unranked Arkansas. You've confused the 1996 SEC title game with the 1995 one; UF's win over the 23rd/24th ranked Arkansas team and 12-0 record that year resulted in their getting blown out by Nebraska in the Fiesta Bowl.
Also what helped Florida wasn't just a win in Atlanta. First, what more helped UF (#4) was Nebraska (#3) losing the following weekend to Texas in the inaugural Big 12 Championship Game (the same weekend as Florida and Alabama played in Atlanta). From the system in play at the time, now ranked #3 and the SEC Champion UF went on to play in the Sugar Bowl, where it was given the opportunity to play #1 Florida State again, in part due to the Rose Bowl still having claim to #2 Arizona State (were it not for Texas beating Nebraska, though, UF would not have been in that game).
And it was #3 UF's beating of #1 Florida State combined with #4 Ohio State's upset over then 11-0 Arizona State in the Rose Bowl that gave Florida the national championship.
Since the Bowl Alliance System was so conference-champion based, UT would have just been looking at a higher ranking at year's end, with likely an Orange or Fiesta Bowl bid instead of the Citrus Bowl matchup.