I doubt any tire shop will balance your wheels 1st before mounting tires on them. I doubt the istalling tech will measure a tire looking for 1/16th of an inch difference in diameter and reject a tire that exceeded it. W/o the eccentricity data then there is no way the tire would be be mounted on the rim as you suggest to minimize rolling vibration. These are things that maybe happen at a NASCAR garage or at your own if you were wealthy enough to own you own tire changing and balancing machines.