Now, as for DoD funding institutional research, absolutely (they funded me last year for something completely benign and outside the scope for "info wars"). They fund research at a lot more places than GT. So, yes, plausible. But, unlikely IMO that NSA has an active presence on your campus doing intelligence work.
BTW, I challenge your claim that GT gets "mostly DoD". I'm sure your school is primarily funded by NSF (the preferred government tit to suck on). DoD is actually a pain in the ass to deal with because they don't go away after the money changes hands. Same is true for SBIR/STTR.
Finally, DoD classifies everything. Don't let that label fool you into thinking the work is sensitive (or even interesting). Within academia, this is less so because the objective of funding institutional research to produce publications. Contract R&D is not something that is popular with faculty (or the school, since depending on the IP ownership, it can put their tax exempt status at risk.)
That said, keep snooping and let us know what you find in that room labeled "no personnel permitted without super-duper top secret clearance".
Is it really that hard to believe? Considering that the Georgia Tech Research Institute (GTRI) gets mostly DoD contracts and research grants and a lot of those contracts are for classified projects.