Neither Kickstart nor UNiTE can write a web.config file. I have had mixed success with it, since some servers seem to require the site to be reloaded on IIS for the web.config to take effect. If you are sure that web.config files take immediate effect on your server I recommend that you wrap the restoration in a BAT or PowerShell script which writes the web.config file before restoration. At the end of the restoration you can delete the file.
If your original site has a web.config file, however, you must not delete the web.config file at the end of the restoration! The last step taken by UNiTE is to restore the original site's web.config file, if such a file did indeed exist at backup time. Therefore in this case the web.config file at the end of the restoration is not the stealth file you wrote with your script, it's the real site's web.config file which should remain intact.
I hope this information helps!
Nicholas K. Dionysopoulos
Lead Developer and Director