In another one of the threads we were discussing how much higher the quality of service was at Costco, because they pay their employees decently and offer good benefits. Similarly here. If 'efficiency' means running things cheaply, then yeah, the postal service would run cheaper if there weren't any unions. If it means efficient delivery and quality service, then no, it wouldn't.
Except we can only have one postal service. Not everyone cares enough about customer service to shop at Costco. The people who simply want to pay as little as absolutely possible will go to Sam's Club or Wal-Mart. They have that option. It would be different if we had to decide as a country between having Costco and having Sam's Club but couldn't have both.