Yes. The high voltage testing can be effectively used for measuring the primary and secondary parameters simultaneously, and thereby calculate the efficiency under actual load conditions while in circuit.
In many countries, including India, the power transformers of capacities from 100 kVA to 500 kVA are rewound after a defect, and these are tested for basic parameters in the factory, which may not truly reflect its efficiency under energized conditions. Thus high voltage testing helps the utilities to quickly check the health of the power transformers very quickly.