Could a lift system like the X-32's have produced a supersonic Harrier in the 1960s?
Short answerPotentially; Britain examined supersonic V/STOL designs, notably the Hawker P.1154 linked to the CVA-01 era.
NotesBritain did study supersonic vertical-takeoff aircraft rather than treating the subsonic Harrier as the end state. The Hawker P.1154 and related CVA-01 work show that the propulsion and configuration question was actively explored, even though no operational successor emerged.