I should add that I mean on a small scale. I'm well aware that World War 3 didn't happen.
Yes. Soviet pilots flew during the Korean War due to the ineffectiveness and poor training of the North Korean and Chinese air forces. It also marks the only period of regular engagement between U.S. and Soviet forces. Their involvement was a closely held state secret as public disclosure would obviously create significant diplomatic issues. It came to the U.S. public eye in the late 1950s early 1960s, here is former Polish Military Attache Pavel Monat disclosing it in Life in 1960. U.S. leadership was aware of the pilots true identity at the time of the conflict, but given the small scale of the intervention and the inability of it to affect the outcome of the war did not publicly disclose the knowledge for fear of forcing broader escalation. There is some evidence that it led decision makers to not make use of the most technically advanced equipment available, in order to prevent Soviet observation of it during something strategic planners regarded as a sideshow to the main focus of the Cold War in Europe.