You must be a member for the duration of the entire tournament assuming you qualify for subsequent rounds. Gambitshark is right. However I don't know if using post cards takes any longer than a server event with 7 or 10 days per move, or as some are, 10 moves in 40 days, etc.
I rememeber one ICCF event before servers when one opponent was from Siberia and another worked on a pipeline north of the Arctic Circle...his mail was flown in once every 2 weeks. I'm lucky I'm not still playing those games.
In any case server tournaments are easier with a lot less bookkeeping and no chance of a recording error or setting up the position wrong.