It could. Question is if there was the ability to keep it from getting out of control. The issue extends way past Cuba. if the U.S. goes in there, the Soviets have the same sort of scenario with Turkey and something of an excuse. The Soviets move on Turkey and you have Article 5 in an eyeblink. NATO had tactical weapons, as well as CW, folded into every war plan.
The other factor to consider is that Nikita Sergeyevich was betting heavy and bluffing his ass off and he knew it. The U.S. had 10 times the throw weight of the Soviets, who MIGHT be able to actually get around 60 weapons onto North American soil (accuracy wise, hitting the Continent was about as far the soviet military could be sure of, and reliability of the 50-75 ICBM in the Soviet inventory was, to be charitable, somewhat sub-optimal). He also had a pretty good idea of just what the SAC brought to the table, all 27,000 deliverable warheads. Khrushchev blinked because he couldn't beat the American hand, and he knew it. Thankfully the U.S. didn't know it, had they been aware of the stunning disparity the pressure on Kennedy to kick the Commies' ass might have been too much to resist.