A QFF member flying only AA and BB would still earn QFF points and SC's; however until they fly four eligible QF/JQ segments no elite status nor any elite benefits will be available.
20.1.5 The travel required in each Membership Year to attain or retain Silver, Gold or Platinum status level must include a minimum of four Eligible Flight Segments where Qantas, QantasLink or a Jetstar Airline is the Marketing Carrier.