Automatic chlorinators such as inline puck feeders, liquidators, peristaltic pumps and SWGs are usually plumbed in the return line after all other equipment.

I suppose that the piping between the chlorinator and the pool, possibly made of PVC or ABS, is subject to high concentrations of chlorine. Would it cause any damage to the piping (cracks, leaks) in the long term?

I would think not, as the concentration is not all THAT high. Its not like you are pumping 6% bleach through them anyway.