If the motor windings are lossless, then no-load for the motor would imply zero active component of current for cylindrical rotor. So the 1.0pu excitation would only provide reactive current, which can never be the min current condition.

For a motor with saliency, the difference between Xd and Xq could change the answer, as some reluctance torque is always involved.

The minimum armature current at a certain constant output power in case of a generator will be always at unity power factor. This minimum value depends on the value of the power.