The automation scheme specified for an Application Configuration is completely unrelated to automating testing against deployed configurations, so it's definitely not your answer.
There is currently no off-the-shelf feature for automating testing tasks. The Quality Center integration is available, but I don't know if it meets this particular customer's requirements. A more general post-deployment automation feature is planned for a future release, probably in the first half of next year. Until then, I'd recommend contacting Professional Services for assistance in how to add custom automation.
Neal