No we wouldn’t.
It’d be a 4-team tie between A&M, Georgia, Texas, and Tennessee.
Since the 4 teams didn’t all play each other and all 4 had the same record against their common opponents (Florida and Mississippi State, which all four teams beat), it would go to A&M would win the 4-team tiebreaker based on conference opponents’ conference win percentage (A&M’s would be 0.4688, UGA’s would be .4531, Texas’s .3906, and Tennessee’s 0.3750).
With A&M separated into the conference’s top spot, it would then become a 3-team tie between Georgia, Texas, and Tennessee…while they didn’t all play each other (Tennessee didn’t play Texas), Georgia beat both and would win the tiebreaker.
(Tennessee would actually then end up in 4th place behind Texas in the end due to the record against common opponents tiebreaker…both played Florida, Georgia, Kentucky, Vanderbilt, Mississippi State, Arkansas, and Oklahoma: Texas went 6-1 vs these teams, Tennessee went 5-2 vs these teams.)