Audition has no ability to play anything, except audio files by hitting the space bar. If you want software that can be triggered externally, you need to look at music composition software with MIDI capability, which Audition doesn't have (it's primarily an editor).
Yes you can certainly make a start with generating noise, but it's more usual to find sounds that exist already and manipulate them using effects, than starting with just noise. I daresay that if you look on Youtube, you'll find tutorials about how people do this.