What happens to a transformer if the supply side is shorted?
Think of a single phase transformer feeding an open circuit on the secondary. The AC is a normal AC signal then suddenly the AC signal instantly becomes 0 V (this represents the short on the primary feed). There will be some amount of magnetic flux (aka energy) in the transformer core that will push a current back out of the primary windings into the 0 V AC source.

If the transformer is perfect in all respects (other than it has a magnetizing inductance), the current will flow into the "0 V" indefinitely BUT there are of course resistive losses so this current will be an exponential decay to zero. If there is no leakage inductance on the primary winding, the 0 V (aka short) will ensure that there is nothing seen on the secondary other than the cessation of the AC waveform when it instantly falls to zero.

If there is leakage inductance on the primary (normal of course) then there will be a small kick-back voltage seen on the secondary due to the magnetizing inductance of the primary not being perfectly shorted to 0 V.

With or without a load it won't make a difference - there will be a small kick-back voltage seen on the secondary as the magnetic flux (and current) exponentially decay to zero.

It should also be noted that if the AC falls to zero volts at the very peak of its waveform, the current in the magnetizing inductance of the primary is zero and no effect will be seen. This is because, at that instant in time, the flux in the core will also be zero. If, on the other hand, the AC voltage halts at a zero-cross (and stays at zero), the flux in the primary will be at a maximum and the effect described above will take place. At all other points the effect will be proportionally less.