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.