According to Norman Friedman in British Carrier Aviation the lifts on Eagle were:
54ft x 44ft and 54ft x 33ft
Her hangars were 63ft or 67ft wide depending upon the reference book, but they all say the hangars were 17ft 6in high. (Incidentally the hangars of all British aircraft carriers laid down 1942-45 had hangars that were 17ft 6in high and IIRC when Victorious was rebuilt in the 1950s the height of her hangar was increased from 16ft 0in to 17ft 6in.)
According to notes I made from Jane's All the World's Aircraft 1964-65 the dimensions of an E-2A Hawkeye were:
length 56ft 4in x folded wingspan 29ft 4in x and height 15ft 11in
Therefore an E-2A was 2ft 4in longer than Eagle's lifts. So no.
However, the Buccaneer, Scimitar, Sea Vixen and F-4K Phantom were all longer than 54ft but had noses that folded and in some cases tails that folded too so that they could fit the lifts. It might be possible to build an E-2K Hawkeye that could fold to fit the lifts.
According An Illustrated Guide to Modern Naval Aviation and Aircraft Carriers, by John Jordan, Salamander Books, 1983 the height of an E-2C Hawkeye was 18ft 4in, which is 2ft 5in taller than the E-2A and 10 inches taller than Eagle's hangars. However, a fictional E-2K Hawkeye might be able to lower its radome to fit inside the hangars.