I'm not sure if there was a fourth TurboEdge, but someone must know for certain.
As for mailing lists:
(1) Certainly, anyone who sent in a registration card...for any TG-16 item...was added to the official NEC mailing list.
(2) It is unclear if NEC and Larry Flynt Publications (TurboPlay) routinely shared mailing lists over the years...but a promo for TurboPlay was included with TG-16 console, so there was some sort of relationship. Why do I bring this up? It is possible that LFP sold/provided TurboPlay mailing lists to NEC, especially before NEC planned a mass mailing.
(3) Anecdotally, once you were on the list, you were on it (from 1989—until whenever TZD stopped sending flyers). The mailing list was a valuable asset transferred over the years... the NEC --> TTi transition (I received promotional videos from TTi). Same for TTi--> TZD (I received flyers).
I should add that I had the same experience with all the magazines (once you were on a mailing list, you were on it until the end).