The "magnetic field lines" are only an abstraction, not much more as an illustrative tool to explain the workings of the magnetic field.
The more exact description of the field of a bar magnet is a vector field, i.e. we have a vector in all points of the space showing the strength (and direction) of the magnetic field in that point.
The magnetic field of the bar magnets is roughly a dipole field, we have a positive pole on the north and a negative on the south (or vice versa).
This field is not defined in the poles because of a division by zero problem.
Thus, the literal answer is that no, the field line doesn't reach the south pole.
However, also this is only an abstraction. The magnetic field of the bar magnet is not generated by some magnetic monopoles in its poles. In fact it is generated by the electrons in the whole bar. The real magnetic field of the bar magnet is more complex as a dipole field. Although the field generated by magnetic monopoles would be quite similar, this is why this simplified version is taught to you.