Had the October War gone nuclear it would almost certainly led to a U.S./Soviet exchange. Of all the proxy wars of the Cold War it turns out that 1973 WAS the closest call. Both the U.S. and, especially, the Soviets misjudged how far the other was ready to go in supporting their Client.
The Soviets had been engaging in direct air-to-air combat with the Israeli for several years before the October War (something that was know to both the Israeli AND U.S. intelligence services) and expected the '73 conflict to go as 1967 had, with the U.S. on the sidelines. The United States, for its part, was not expecting the Soviets to make threats of direct intervention, even (perhaps especially) after U.S. aircraft had established an airbridge providing resupply of the Israelis from Reforager sites in Europe.
As has been noted, the U.S. actually had airborne forces IN THE AIR before the Soviets blinked. The U.S. had also moved 6th Fleet units into the Eastern Med, once there the CBG's became part of the SIOP, and the results of any attack by the Soviets on SIOP elements does not bear considering.
In short, forget about the Israeli Skyhawks, worry about the ICBMs.