Air support would not have been enough to save the invasion. As Jeffrey Record writes in *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 Castro 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. Of course, if the exiles had not just air support but the support of US ground troops as well, the result would have been different, but in that event, why start with an exile invasion to begin with? And it is arguable that even a "successful" invasion would be a bad thing for the US: see my post at
https://groups.google.com/d/msg/soc.history.what-if/DQFyp4RcAUQ/ErKyse2Ms3MJ