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The "sound barrier" is a term chosen for dramatic flair to describe the increase in air resistance as velocity approaches the speed of sound in that air.
The speed of sound in air is definitionally the maximum speed a which a compression wave can propagate through that air. As you move forward at faster and faster speeds, the air in front of you has less time to move out of your way as you approach the speed it can compress. That increase in resistance constitutes the "barrier". Exceeding the speed of sound thus results in that "barrier" transitioning into a conical shock wave propagating outward from the object traveling at speed. (All of that is rather simplified.)
So, no. From Felix's perspective, he experienced a significant increase in air resistance as his speed increased, transirioning to a relatively consistent degree of resistance with a conical shockwave which he may or may not have been able to perceive from the point of view of being its origin as he accelerated beyond Mach 1.
He would likely have needed to consult instruments to know he had reached that kind of speed.