Does the sound barrier apply to a silent aircraft?
The sound barrier has nothing to do with the noise the aircraft makes. It has to do with the fact that if it is going fast enough the air can't get out of the way. This creates a shock wave where the aircraft is pushing the air aside. A shock wave is where the speed of the air transitions from faster than sound to slower than sound and involves the release of considerable energy. You can control the shockwave to some extent by careful shaping of the surfaces, but a plane going fast enough can't be silent. 

You can make very quiet sub-sonic aircraft, but they tend to go slowly so that the noise of the air flowing over the craft is minimized.