"Does it help to fly for a company that is subcontracted out by FedEx or UPS for the increased possibility that I could get an interview with one of them down the road?"
Though I did, I don't think, in this day and age, that it helps much.
It's about experience and who you know. Get the right experience and know the right peeps, and you have a shot.
That's the way it is.....good luck.