NO!

During the height of the Cold War US airlines flew over Cuba EVERY DAY, and still do today. (in fact the US supplied Cuba with it's radios and even it's air traffic control radar as I recall for it's Air Traffic Control System just so airlines could do those overflights, even during the cold war - we did that since Cuba could not afford the equipment)

Civilian Aviation overflights of countries that are somewhat opposed to each other have been a regular fixture of Aviation for decades. Russia, China, North Korea, and during the Vietnam War, North Vietnam have been the only large exceptions to those overflghts over the last 70 years.