No.
Freepmail does not automatically make the entire conversation available to all those given access, nor does it automatically list the others who are taking part, nor does a chain of freepmails collect every message in chronological order with linkbacks--just to suggest three reasons.
Why do you even care what people are doing on another site?
OH, I see. Freepmail is private between two individuals, sort of like M. Thatcher’s Freepmail to Jim.