If you're on an EK flight departing LHR, BA will not through check your bags. Makes no difference if its a QF codeshare, unfortunately.

It would be for you to decide if it is worth the risk. If your LHR-MEL ticket is restricted, you would be at the mercy of EK's goodwill to rebook you. BA wouldn't get involved, and probably neither would QF if you have 'noshowed' your flight.