I hope you don't mind, I converted your support ticket into a public forum post so that all of our customers can benefit from the answer to your question.
Is there a way I can ensure these app.config settings are still applied during the running of the tests?
In short, no there isn't. The problem arises from how Test Studio dynamically loads dlls referenced by the test at run time. The dynamic loading process bypasses the normal .NET mechanism that would load the app.config for that dll.
We wrote this code sample to demonstrate how you can overcome this limitation.
the Telerik team