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If the xfmr secondary is a wye with the center point grounded, then yes, you would read 277V to ground on each phase.
How would 277V loads in the building be connected if no neutral was provided though?
If the service is straight 480V delta, then the voltage to ground will depend upon how (and if) the secondary on the transformer is grounded, e.g. if corner grounded (i.e. one leg of the three grounded) you would see a full 480V to ground on the other two phases, or if the secondary is ungrounded the voltages to ground could vary quite widely.