vixenradio -
Actually, not everyone working at national HQ's have to be alumni of that organization. (as evidenced by the fact that two guys work at my sorority's national HQ) If you are interested in doing something like that, I would check and see if any groups have HQ around your area. In my opinion, you would be a great asset since you already have a knowledge of Greek life, the Greek alphabet, etc.
Same with any of the umbrella groups like IFC and NPC. Good luck and let us know if you find anything!