Unfortunately the fare rules don't determine the flight booking class bucket. There is some linkage but it's not a 1:1 corespondence.
Once you have booked you can see the class, but I don't know how to do it beforehand on Amex Membership Rewards bookings, sorry.
If you ring up Amex Travel you can ask the agent if they can tell you the booking class, but that is for cash bookings.
You can convert membership reward points to Avios and book a flight on BA.com, those will definitely not get any TPs or Avios.