Has anyone developed an API interface to Archicad publishing so that publishing can be automated to publish on a schedule?
Yes and No
Tibor Lorantfy of Graphisoft developed a Python Script that will periodically publish from Archicad. The Problem is that Archicad must be open at the time.
His script is published on his GitHub site
Using Window's or Mac's schedulers, you could automate this but would sill have the problem of leaving open Archicad which would require additional configuration to handle.