I’ve not done this. But by glancing at the source code, I agree it should be doable. Not sure how straight forward it will be. Partly depends on how tightly integrated you want it to be.
I would start with the stand alone version and convert the root index.php file to a main WP plugin file, copying everything into the plugins folder. Be sure WP_DEBUG is set to TRUE. Activate the new plugin and see what happens :). Hopefully nothing, meaning there are no obvious name collisions and other such conflicts.
You would eventually want to combine user management, but for now manually add some WP users to the Chat system for testing. Hook into the ‘authenticate’ filter in order to log WP users into Chat as well.
You should use the same DB for WP and Chat so eventually you can do all Chat DB functions with $wpdb methods so there is only one connection. For now let Chat create its own.
Not sure how Chat really works, but I imagine you’d want to eventually make Chat templates work as page (post type) templates. For now, the Chat templates alone might suffice.
If you’re familiar with any of the supported forums, examining how integration was achieved would be very helpful but not required.
This would be a start at least. Achieve a minimal integration and see how things work. Incrementally tighten the integration, testing as you go. You should get it all eventually. Good luck!