There is not, to my knowledge, either convention or written law on who can speak and advise the Governor General. I've advised the Governor General, and I'm sure as hell, as a professor, not mentioned in any law or convention. The Governor General gets advice, seeks advice, from a number of sources. I'm not even a lawyer.
As to whether it would be proper for the Governor General to hear advice from the Speaker, in my view, it's just fine. I think the Speaker has to think carefully about it, because if the Speaker is getting into a hot political issue and the Speaker's legitimacy.... We know that we've evolved the office of the Speaker so the legitimacy is based on the consent of the various parties of Parliament, and it's seen to be a position that's independent of any partisan affiliation. So I think the Speaker would have to think very carefully about going out.
Anybody who thinks letters addressed to the Governor General don't arrive and get read should be very careful about asserting that unless they have very strong evidence. The premise of your question, that the famous letter, which millions of Canadians actually saw in their newspapers and on television, never got the eye of the Governor General, to me is a pretty outlandish kind of possibility.
But if you want to assert that, then I think you should check it out.