When a plane flies faster than the speed of sound, does the distance between plane and sound increase?
I think you are missing some physics knowledge, so let's start from here:


  If a plane flies faster than the speed of sound


Sound is a compression wave that travels through air. Given a certain air temperature, the sound will travel at different speeds through the air.

If a plane flies faster than the speed of sound means that the compression waves it is generating will remain behind the aircraft:



image from here


  will he be able to overtake his own sound and hear itself?


As you can see on the right picture, if the aircraft is travelling faster that the speed of sound, the compression waves it generated in the past will remain behind. If it would stop/slow down, the waves would then catch up with the plane and a person on board would be theoretically capable of hearing them.