Is there any induced current in the pickup coil when the polarity of the bar magnet is flipped?

Faraday's law , he direction of the magnetic field changes by 180º, in the polarity inversion processes, induces a voltage.  

Explanation:

For this exercise let's use Faraday's law

          E = - dФ / dt

          Ф = B.A = B A cos θ

where B is the magnetic field, A is the area and θ is the angle between the field line and the normal to the area.

We can see that an electromotive force (voltage) is indexed when there is a variation of the field B, a variation of the area and change of the angle or when there is a combinational of them.

In this case, the magnitude of the field is constant, as the wire is rigid metal, the area is constant, but the direction of the magnetic field changes by 180º, in the polarity inversion processes, for which reason each change induces a voltage.

If a voltage is created in the ring, which has a resistance, a current is also generated in it.

Therefore the answer is If a current is created in the hoop