White Georgians at the time were pretty evenly split on the question of secession; in the popular vote for delegates to the convention, the immediate secessionists won by the thin margin of 44,152 to 41,632. (discussion here).
Five years later, Alexander H. Stephens, a member of the convention (and then vice-president of the Confederate States of America), talked about support for secession in the state:
In some of the mountain counties the Union sentiment was generally prevalent. The cities, towns, and villages were generally for secession. The anti-secession sentiment was more general in the rural districts and in the mountain portions of the State. Yet the people of some of the upper counties were very active and decided secessionists. There was nothing like a sectional division of the State at all. For instance, the delegation from Floyd county, situated in the upper portion of the State, was an able one, and strong for secession; while the county of Jefferson, down in the interior of the cotton belt, sent one of the most prominent delegations for the Union. I could designate particular counties in that way throughout the State, showing there was nothing like a sectional or geographical division of the State on the question.In the Civil War, of course, secession lost big time.
