Maybe. Trouble is that the competency profile for an optimal TSA officer may be very different than what you want/need for an armed officer.
About a decade back, I attended a talk by a Swiss cognitive psychologist, contracted by the Canadian equivalent of the TSA, on how they assess and select baggage screeners. VERY impressive, and a very unusual set of skills. I thought drug-sniffing dogs were special. These folks are extra-special. Being able to identify individual bomb-making components stuffed in between electric razors, or underwire bras, or headphones, or laptop chargers, or sextoys,...in an x-ray, is not the sort of skill you easily run into on the street. Can you find folks with those skills in the same package as someone willing and able to responsibly handle a sidearm? I don't know.
That's the problem with reactive policy; we're motivated to think that some things are easier, and less problematic, than they might actually be, and less motivated to look exhaustively for the niggling details that cause those problems.