"Does he or she answer?"
Translation:Svarar han eller hon?
No, it can't be allowed since "hen" would only refer to one person. In this case we have two persons (who clearly define themselves as male and female) and we want to know which one of them answers.
Svarar hen? Would only be a question about whether that particular person who either is of unknown gender or defines "hen"self as a third gender, i.e. neither male nor female, is answering.