in short: yes it has to.

A balcony railing must be designed to hold the weight of a person, preventing it from falling off a balcony. That’s what all building codes in Europe mandate in one way or the other. A plugin solar kit weighs between 15 kg and 60 kg. In any case this is less than the weight of an adult person, and your balcony railing must be able to hold it.

If you have doubts about the solidity of your balcony railing, consider replacing it. Your building code might require you to do so anyway.