The approach you're talking about (using exported functions) is not going to fly. The simplest form of communication between two Win32 programs is to have them use SendMessage or PostMessage to talk to each other. Locating the window handle (usually by window class name) is step 1, sending a message is step 2.
Secondly, DUnit gets you nowhere near your goal, and TTestCase cannot be extended neatly to be a GUI Controller as that's not what it's for. It's for unit testing. Round peg, square hole. Write TTestCases for classes you can hive off and test, and use DUnit to provide test coverage for those parts of your system that you can provide test coverage for.
For UI testing, use a completely separate framework. There are two basic approaches done by Delphi programmers for automated integration tests of the sort you're proposing.
A custom hack job. Such is what you are describing. Inside Embarcadero, there exists a framework which is called Zombie, something Nick blogged about back in 2007. Its approach is based on several kinds of "primitive IPC", usually involving a Win32 SendMessage or PostMessage window message from outside the program to a window handle of a control inside the program. However, the internal code IS SIGNIFICANTLY MODIFIED to permit zombie testing. No you can't have Teh Codez, they're internal and proprietary to Embarcadero. But it does illustrate that the approach does work, and does not require rewriting the whole application or writing a huge number of mock-classes, like unit testing would have done. If you want to go down the hack route, you will be writing your own User Interface Testing Framework, which should probably be completely separate from and use no DUnit code. You are welcome to try, but I'm telling you, it's a serious impedance mismatch. If I was starting my own custom framework in 2013, it would be DCOM based, because Delphi DCOM server code could be simply conditionally compiled into many programs, and DCOM would handle the function call "marshalling" details for you. I suspect I would get a year into the project, and I would give up, because in the end, I doubt I could make any system (DCOM or Win32 message based) pay off.
A complete external testing tool which you write test scripts in, like AutomatedQA/SmartBear TestComplete. Your tests would not be compiled into a delphi test program, but run inside TestComplete, and Pascal-like script syntax is just one of the available options for writing your test scripts.