There's also other "Tech" schools like VT and Texas Tech. Sure GT is a more prestigious academic institution than those two but the "Tech school" sterotype is no excuse for not competing in athletics.
Not sure what point you are making, but the there is competing in athletics and then there is competing in D1 athletics.
Tech, like so many other "Tech" schools, was founded to help industrialize the state, especially after the Civil War. You could argue that Auburn is just like Tech and therefore, there is no reason why Tech can't compete with Auburn.
But the schools have evolved completely diffenerently. Athletics at Auburn is fundamental to the mission. It is everywhere. Students are encouraged to participate in sports, athletics, fitness ... and athletics is used to unite the alumni base as well. Auburn is dysfunctional when it comes to running the athletics department ... but they want to win and have the money to throw at it.
That *may* have been true earlier at Tech (prior to say, 1980), but ... Tech today is WAY beyond being a typical technical school. It's focus today is heavy on research and delivering $1B a year to the state of Georgia. Tech's peer group today is ... MIT, UCLA, Johns Hopkins, Texas A&M, Princeton, CalTech, Yale, Cornell, Emory, Stanford, etc. (All top 10 research universities). If you are the President of GT, THAT is who you compare yourself to ... and one reason why Bud spent about 15 min a year on athletics.
I'm extremely proud that Tech is one of the Top 10 research universities in the country and one the few that still do compete at the D1 level. But don't forget ... Petit almost shut athletics down. It wasn't a priority for the Hill then and it hasn't become one now. It's research $$$.