Does Audition support Rewire VST?

I know this is an old question, but I had an answer to this back in 2013, and it's a bit roundabout.  First, Adobe did not abandon MIDI.  MIDI was not part of the original sound app they bought.  At the time it was more like audacity, built with virtual studio technology for processing by output, not by input, which is half of midi capability on each.  MIDI "DOES" work with similar technology, but as an extension of it for instrumentation, an acronym rightly called VSTi, the small i denotes the addon nature of the technology.  REWIRE is a separate technology that is largely based on the same capability.  Essentially, REWIRE uses technologies like ASIO or ALSA to link audio tracking between running applications, tying outputs of one into the tracks of another as an input.  While AUDITION does not directly support REWIRE technology, it DOES support ASIO natively.  It also supports native windows sound driver formats.

This gives us two ways to interface with AUDITION in much the same way as MIDI or REWIRE.  First, you can download a virtual sound driver like ASIO4ALL that allows you to select several sound devices to tie together as one, and utilize this driver in the sound hardware setup of AUDITION.  This does alright, but has a tendency to "Select itself" as your default driver, and can interfere with any advanced sound tech you have, since it takes exclusive access to your devices.  There may be some odd effects on the rest of your system.

Another way is the VSThost application.  I don't know if it is still in development, but it comes with a plugin called Legree, which, when used as a VST on a track, allows you to rewire that track only.  This gives you a single track where you can feed audio in from outside, in the VSTHOST application.  You can have Input to the track enter into the VSTHOST, go through a set of processing, and come back out onto the track during recording, or you can feed the track from VSTi\MIDI being fed into the VSTHOST app.  Again, this works only one track as far as I've seen, but I rarely need more than that.

One interesting added bonus I've found is that there is a Playback plugin that works with VSTHost that allows you to queue up a list of playback tracks, and play through them during recording.  I've recorded shows using this, feeding the playback out over a mono output to the main sound system while putting out the rest to a submix that is muted to prevent any crossplay.  This has allowed me to capture an entire set of mics, monitor them in different ways without affecting the output system of the house, and clean a few things up before they became a problem.

Audition is a simplistic DAW meant more as a companion to Premiere than a full featured DAW.  It allows you to tighten your focus on your audio outside of Premiere, while others work on the video inside Premiere (dynamic linking capability).

Audition has not used Rewire since version 3, when it didn't work very well anyway. After the complete rewrite it was dropped, along with everything else MIDI, so I'm afraid that there's no way you're going to get it to work at all - as a simple Google search would reveal.