I don't think it necessarily butterflies away the F-14, but it might cause a similar aircraft to come along later than historically, which would likely be a better aircraft than the F-14.
When it became apparent in the early 60s that the F111B would go ahead the Navy started the VFAX competition to replace the F4 and A7 in the escort/air superiority fighter and ground attack roles, working alongside the F111B in CVWs. The 1966 VFAX spec demanded it be able to beat the Mig 17 and Mig 19 in close combat, and the 1967 spec demanded later Soviet fighters, as well as undertaking the attack missions of the A7.
In parallel Grumman was working on the F 111B, trying to reduce weight, AND was contracted by the Navy to undertake studies of advanced fighters. In the event the VFAX proved to be a dud, not better than the F4 as a fighter or the A7 as an attack aircraft. In the process Grumman came up with design 303 and in 1967 reworked this design to include the AWG9-Phoenix system without ruining the ability to defeat the Migs in close combat.
As a result, bearing in mind the problems with F111B which was pushing it towards inexorable cancellation, the Navy was presented with the answer to both of its problems; a replacement for the failing F111B and a replacement for the F4 in the escort/air superiority role. The F111B was cancelled in July 1968 and a month later the Navy issued the VFX requirement written around Grumman design 303. 6 manufacturers submitted proposals but Grumman's 6th refinement of 303 won the competition.
I would think that until 1967-8, as the 303 evolved into the F14 and the F111B was plummeting toward cancellation the Navy planned to replace the A7A with the VFAX in the early/mid 70s. At about this time the USN gave the OK to re-navalise the Spey powered USAF A7D into the A7E, giving the A7 a new lease on life and providing the improved light attack aircraft that the VFAX re-write into the VFX now made necessary.
HOWEVER
If in 1962 the Navy wriggled out of the F111B and into the Vigilante then the impetus to squeeze the AWG9/Phoenix into the Grumman model 303 doesn't exist and the USN soldiers on with the unsatisfactory VFAX competition which isn't much better than the F4/A7 that it was supposed to replace. In contrast the F14 is obviously better than the F4 and F111B and although we can't know for sure almost certainly the F5 Vigilante-interceptor.