Yes, he might. If Dr John is into Japanese pop culture or is a fan of modern literature, there's a good chance he has a light novel. Light novels are quite popular these days.
Since we don't know the exact story, it's difficult to name the key elements. However, common elements in a family - related story could be relationships, like love or conflict among family members. There might also be family traditions or secrets.
I haven't come across any information suggesting that 'Dr. John' has a corresponding light novel. Usually, such adaptations are announced or mentioned, but not in this case.