Can current flow to earth in TN-S Earthing system?
It all depends on where the short occurs.

If one of the three phases (A, B or C) shorts to the equipment frame, then the circuit will be made through the PE conductor.  No current flows to earth there.

However, it's also possible for a phase to short to something that is itself grounded, but not connected to any PE conductor.  That thing might be a water pipe, or even a person.  In that case the ground itself forms part of the return path to the transformer's earth.