No, Georgia has been to Atlanta three out of the last four SEC championships games. UGA was only recently there if you are the kind of person to use "kinda" has a a word.
Florida hasn't won it all since Tebow was in college and Georgia has been building up year after year in recruiting and on the field progress. You said "just a few good seasons" yet, when in the hell is making Championship games "just a few good seasons?" To me, the 3 SEC championships games, two CFB appearances, and wins at the Sugar, Peach, and Rose bowl are more than "good seasons".