Could we answer this by removing email from the question?

If I go to a lawyer and ask them a question in person, seeking legal advice, even if they don't response and just show me the door, is what I am saying protected? I would think yes.

If I ensure my lawyer is in every single discussion I ever have with anyone else, just to say all my discussions are protected, what would happen? I assume that wouldn't work and there is already a standard on how to handle this for in person meetings.

Shouldn't that same standard be applied to discussions happening through email?