No, an aircraft would not be able to travel backwards by flying against the wind if the wind speed exceeded the speed of sound. The speed of sound is approximately 343 meters per second (or 1,125 feet per second) at sea level under standard conditions. It represents the speed at which sound waves travel through a medium, such as air.
In the scenario you described, if the wind speed were faster than the speed of sound, it would create a phenomenon known as a supersonic headwind. When an aircraft flies into a supersonic headwind, it would experience significant aerodynamic challenges.
When an aircraft flies faster than the speed of sound relative to the air around it (supersonic flight), it generates shock waves and encounters a sudden increase in drag and other aerodynamic effects. These effects would make it extremely difficult for the aircraft to maintain controlled flight or sustain any forward movement against the supersonic headwind.
In practical terms, it is not possible for wind to blow faster than the speed of sound in Earth's atmosphere, as the speed of sound sets an upper limit for the speed at which disturbances can propagate through air.