So, I wanted to throw this out to the Hive Mind here. Is there actually tools that allow one to do automated testing for Desktop apps?
Just as with web applications, for automated unit and integration testing you would decouple the business functionality from the UI. The MVC or MVVM models popular in web applications absolutely apply to desktop too, so all the .NET unit test and mocking frameworks can be used for that. NUnit, MSTest and so on.
I suspect what your IT guy meant was automated testing of the actual UI functionality, as you would do with a web app by automating a web browser using Selenium or something. Free tools exist for this, such as Winium or Microsoft's WinAppDriver. Although I'd be of the opinion that this is what User Acceptance Testing by humans is for.