Running Audition in Wine (in Linux) would be a bad idea. It may work, and it may
seem like it's working well, but you would have all kinds of latency issues, as well as hardware/software issues. Linux has its own way of handling sound (JACK, ALSA), which is 100% different from Windows. If you really want to run a Linux box (and I don't blame you), check out
Ardour.