This is really important, yes. It puts him in the tradition of other early Genuine People Personalities. Eliza was a psychiatrist (you expect her to reveal nothing about herself and always bring the conversation back around to your statements). Parry was a schizophrenic (you expect him to speak in non sequiturs and obsessive repetition).
I hadn’t thought about this, but it’s smart in a couple of ways. It lets you imagine that Floyd is off doing something, which implies motivation and agency.