In the same way with a turbocharged engine, where with the turbo producing the majority of the power, you can shut down the reciprocating element and cruise on the turbo alone? I think not!
Doesn't the J58 merely enable the aircraft to achieve operation in a regime where the inlet magic and bypass ramjet elements start to work - just as a turbocharger uses the gas generation of the reciprocating engine to start its work when 'starting conditions' are met? Poor analogy, I guess - in fact probably anal-ology!!. But wasn't the Napier Nomad supposed to do something really clever and achieve excellent SFC by using a compound reciprocating/turbine system? We had one at my university - a great big lump of metal with a fiendishly complicated design which was rendered obsolete by far simpler turbojet and turboprop engines!