I haven't conducted any sort of study about the office of the Speaker and the relationship between the Speaker and the Governor General. But with that disclaimer out of the way, I don't see anything objectionable about the Speaker approaching the Governor General to provide information, provided that at all times we're very clear on this distinction between providing information and giving advice in the constitutional sense. That latter function is the exclusive preserve of the Prime Minister.
That's really all I can say about the issue. Does that answer your question?