Hi Jen,
I am not sure if you need the published site or if it is a tool for the synchronization.
If you want to synchronize the physical files, you can use an external tool. You can see a comparation of those tools here:
http://en.wikipedia.org/wiki/Comparison_of_file_synchronization_softwareMore information about pre-compiled Kentico sites is here:
Publishing sitesI am not sure what kind of errors you get if the site is updatable. However, then you could update .aspx files. If it is not updatable, then you need to publish the site every time you need to change a physical file. Please note that the published web sites should be the sites with the finished development.
Best regards,
Helena Grulichova