This would actually be going against Stalin's whole strategy:
"Contrary to popular belief, the purpose of the Berlin crisis was to reverse political decisions already taken by the Western powers, not to force the Western garrisons out of Berlin--although the latter was a long-term Soviet goal. Stalin hoped that failure in Berlin would humiliate the Western powers and force them and the Berliners to accept Soviet aid and Soviet terms. It is clear that the Soviet leader did not want war with the United States. He was committed to attaining his goals using every method available short of an action that would provoke the Western powers."
https://apps.dtic.mil/dtic/tr/fulltext/u2/a433271.pdf
Besides not wanting war, the other reason Stalin would be very unlikely to do this is that for a long time neither he nor the West thought that Berlin could in fact be supplied by an airlift. The airlift had been instituted as a stopgap measure--to buy time for the West "to seek a diplomatic solution to the crisis posed by the Soviet blockade. It enabled them to negotiate without either the need to give in at some point to Soviet pressure, or to escalate the situation beyond control.... [N]o one including Bevin and Clay, planned for the airlift or foresaw that it could become that expedient. It was a logical device implemented by military leaders in Germany as an immediate response to the situation. Clay had used it on a limited scale during the April crisis, and he resorted to it again in June almost as a reflex action...Finally, and most important of all, the airlift fitted into the prevailing written and unwritten ground rules already established through previous interaction with the Soviets in Germany. Tacit agreement to act within those ground rules was all important: it prevented the situation from escalating into something neither side wanted--a war in Europe." Ibid.
A more plausible (though still unlikely) way for the situation to lead to war would be by trying to send an armed convoy via the Autobahn to break the blockade, as Clay and Robert Murphy recommended:
https://www.alternatehistory.com/fo...in-blockade-was-enacted.454005/#post-17746025