How can I configure Adobe Audition so that it loads a specific session when it starts?
It doesn't seem to be directly possible:
Is it possible to execute scripts on wav files using command line parameters?
If not, is there a way to automate script execution on files without opening the Audition interface?
No it isn't, I'm afraid. There was a discussion about this some years ago, and the upshot of this was that it might be possible (and probably is, if you put the effort in) to use a third-party batch processor to provide the virtual keystrokes for you. But that's about as far as it goes.
Source Command Line Parameters | Adobe Community
And:
You might want to investigate Adobe's automation platform, Adobe CEP Extensions.
Source Comment on automation - Automating audio processing in Adobe Audition - Video Production Stack Exchange
Adobe CEP Extensions, and developing add-ons for Audition
With the CC 2015.1 release of Audition, we implemented support for
third-party integration via the Adobe Context Extensibility Platform
(CEP). This technology allows anyone with some HTML and JavaScript
know-how to build integrated panels that extend or supplement the
functionality of Adobe applications, offer access to third-party and
web technologies without leaving the applications, and allow those
services to share Application data and files back-and-forth. There
are already over 1600 addons available for Adobe desktop applications
such as Premiere Pro and Photoshop.
Source Adobe CEP Extensions, and developing add-ons for Audition | Creative Cloud blog by Adobe