Top 20 all-time CFB program, won a National Title this Century and played for another. Hell, they have been a lot stronger in the modern era than Tennessee and they have an ALL-TIME winning record against Tennessee.
There are 6 power programs in the SEC historically: Alabama, Auburn, Florida, Georgia, LSU, and Tennessee. Out of those 6, Tennessee has been the weakest link and arguably the one that people say shouldn't be a power program (I still think we are).
Auburn can and has played for National Titles. Ole Miss hasn't. Auburn is a MAJOR step up from Ole Miss and there is precedence, Tommy Tubberville left Ole Miss for Auburn.
Actually they paid $180k for that NC