The way in which I was able to bypass the GUI password prompt and still use with administrator privileges
was to recompile the Automator app and supply the user and password in-line:
on run {input, parameters}
set myCommand to POSIX path of ((path to me as string) & "Contents:Resources:script_name.sh")
do shell script (quoted form of myCommand) user name "local-admin" password "local-adminpassword" with administrator privileges
return input
end run
This accomplishes running the Applescript as with admin privileges, but without popping up the GUI password prompt. The app then runs silently, as I needed, and runs the script script_name.sh which in turn runs many other scripts and copies over other resource files out of (from myapp.app/Contents/Resources/) into system directories etcetera.
For the record, I needed it to act this way because I am deploying this app using Munki and wanted it to automatically run silently after install using a postinstall script:
#!/bin/bash
open -b "com.company.bundleidformyapp"
exit 0