That's an interesting thought, rubesl. Didn't realize the background check was more comprehensive. Often1, I already had PreCheck, paid for by my company. Have some international travel this year, which is why I (and my wife) decided to get GE. My AmEx plat card paid for it, finally getting some use out of the benefits!
I think I will update my Southwest profile with the GE # and see if I notice any difference. I fly them two or three times a month, and am 100% with my PreCheck # getting PreCheck.
Stay tuned - will report back.