Currently, this is not in the short-term planning for Audition and most Adobe applications. Historically, this has been partly because the market has been too small to justify the development and licensing costs to support Linux. However, I think Linux adoption has been trending higher and higher over the last several years, and with Android and similar platforms, I suspect Adobe will start dipping their toes into the Linux waters in some way. This can already be seen with Adobe Connect Mobile and their Photoshop.com services, though they did recently announce they were dropping support for Adobe AIR on Linux to focus on mobile.
In any case, I'll note your request in our database. (There's already a request for Linux support, so I'll add the URL to this post in the notes.)