crab: when setting up a TRA / TDA I normally inform the local ATC unit who maybe giving a flight information service to GA in the area, and follow it up with the paperwork later. But in class G airspace not everyone will be in receipt of such a service (due to a number of reasons), so do not expect everyone to get the message.
I fly for the police in the southern UK and it is not unusual for GA to join me (while orbiting an incident) to see what I'm looking at