As a group we kinda do some drills at the beginning of the season and every month or so we're out locally: search & recovery, search & rescue, 02 administration review - lots show up for that one
It's a lot of fun and everyone gets to practice rusty skills.
& to answer the original question, yes Instructors should be certified rescue (bare minimum), because never-ever students trust them completely with their life in a foreign environment. Big resposibility.