O.O.C.OOC. Would the RN have known about the power of the BS6 catapult in 1961 when they were deciding to put Speys in the Phantom, because at that time the RN was using 103' BS4, 145' BS4A, 151' BS5 and the Eagle was getting the first 199' BS5A? The BS6 was going to be 250' and have more power than the BS5A so as you say the Spey wasn't needed for the launch although it would probably have still been needed for political reasons.
I think they would have because work on CVA.01 began in 1960 and F-4K wasn't approved until 1964 after the 2 year P.1154RN interlude. Furthermore the specification for CVA.01 included the ability to operate 30 OR.346/ER.206 variable geometry superplanes, which in the early 1960s were planned to replace the air group of 36 Phantoms and Buccaneers in the 1970s.