We had a jumper on our cruise ship on a transatlantic. Sea conditions were favourable and there would have been a good chance of a successful search by LRMPA. The idiot was very lucky to be found, in the pitch dark, by one of our fast rescue craft.
Had we not found him then an aircraft search would have been essential for quickly covering a large area.
As for ASRA, the AEW Shacks also carried ASR although I don't think it was ever used but I am sure a downed F4 crew would have been pleased to see it. On Nimrod there were occasions when all ASR and life rafts were dropped and were essential to survival pending rescue. The Nimrod was also better as a search platform than a Sea King which could then maximise its endurance for rescue.