I agree with Jeffrey Record, *The Wrong War, Why We Lost in Vietnam* (Annapolis, MD: U.S. Naval Institute Press, 1998), p. 171:
"It was clear at the time that the invasion could not possibly have
succeeded without American air support. But it was no less clear to many
at the time, as has been the judgment of almost every retrospective
analysis, that the invasion would have failed even with that support. The
argument over Kennedy's decsion is irrelevant because the premises and
planning of the Bay of Pigs invasion were so faulty that no amount of air
support would have made a decisive difference. Aside from the invasion's
fatal lack of secrecy and violation of every principle of amphibious
assault, it was ludicrous to expect a force of fourteen hundred to hold its
own against the twenty thousand Cuban army regulars and local militia that
Castro could--and did--assemble to lock the invaders down on their
beachhead. But an invasion of ten times as many exiles would also have
beeen dooomed from the start because of the CIA's disastrous assumption
that Operation Zapata would spark a mass popular uprising against the
Castro government; the CIA apparently assumed that Casto was as unpopular
at home as he was in the Cuban exile community in the United States. In
fact, in 1961 the Cuban Revolution and Castro were still immensely popular
on the island. Cuban communism's appeal...rested first and foremost on its
nationalist credentials, and Castro was swift to exploit the Bay of Pigs as
yet another Yankee bid to reenslave Cuba to American capitalism. In the
final analysis, it made no difference in April 1961 what the USS *Essex*
did not do off Cuba's shores."
http://books.google.com/books?id=VRekjjSA5uIC&pg=PA171
(Even if one thinks that Record is exaggerating Castro's support in Cuba in 1961 and instead attributes the lack of a popular rebellion to the efficiency of Castro's security police, the result is the same.)
The only way to "save" the Bay of Pigs is with a massive invasion by US troops. But if you're going to do that, why start with a rebel invasion in the first place? It would be like starting Operation Iraqi Freedom with a token invasion by Iraqi rebels. In any event, the attention given to air support is way out of proportion to its military significance.
As for what would happen if there was a massive invasion by US troops, I'll recycle an old soc.history.what-if post of mine:
***
It's very
unlikely that Khrushchev would go to war as a result but it is likely that
he would feel a need to do *something.* I once proposed a scenario in
which his response is to do what in OTL he did a few months later anyway--
build the Berlin Wall--and I noted that then people would be speculating in
this newsgroup "What if the US had never invaded Cuba? Would the Berlin
Wall have been built?"
One may doubt, incidentally, that a "totally sucessful" invasion (in the
sense of one which would actually overthrow Castro) would be a good idea
from the viewpoint of *Realpolitik*, even if there is no serious reaction
from Khrushchev. It would entangle the US in an extremely messy Cuban
political situation: (1) The anti-Castro factions would be struggling
against each other for power, and the US would have a hard time being
neutral; (2) the new regime would be seen as a puppet regime even by many
Cubans who were not Castroites; and (3) there would likely be guerilla
warfare and terrorism by Castroites. Moreover, such an invasion would be
extremely unpopular in Latin America, and anti-Yanqui feeling could grow
tremendously, so that the US in destroying one Castro might create several
new ones.
No doubt Clayton Fritchey, then an aide to Adlai Stevenson, had some of
these things in mind when he told JFK, "Mr. President, it could have been
worse." "How?," JFK asked. Fritchey replied, "It might have succeeded."
(Jim Rasenberger, *The Brilliant Disaster: JFK, Castro, and America's
Doomed Invasion of Cuba's Bay of Pigs,* p. 395.
http://books.google.com/books?id=0Ex08ZkkXEkC&pg=PA395 )
https://groups.google.com/d/msg/soc.history.what-if/DQFyp4RcAUQ/ErKyse2Ms3MJ